{"id":966,"date":"2025-04-06T16:22:35","date_gmt":"2025-04-06T16:22:35","guid":{"rendered":"https:\/\/topperpoint.com\/?p=966"},"modified":"2025-04-06T16:22:35","modified_gmt":"2025-04-06T16:22:35","slug":"linear-equations-tips-tricks-and-shortcuts-for-solving-questions","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/ebook\/linear-equations-tips-tricks-and-shortcuts-for-solving-questions\/","title":{"rendered":"LINEAR EQUATIONS : Tips, Tricks and Shortcuts for Solving  Questions"},"content":{"rendered":"<p>Questions of Linear Equation can be solved very easily through short trick shot techniques, we will try to explain to you today through our articles that how you can solve the questions of Linear Equation correctly in very less time. We will tell you what is linear equation, how to solve linear equation and how to understand the questions of linear equation, these questions are from linear equation and you have to request it, today we are going to talk<\/p>\n<p>\u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0936\u093e\u0930\u094d\u091f \u091f\u094d\u0930\u093f\u0915 \u0936\u0949\u091f \u091f\u0947\u0915\u094d\u0928\u093f\u0915\u094d\u0938 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092c\u0939\u0941\u0924 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0939\u092e \u0905\u092a\u0928\u0947 \u0906\u0930\u094d\u091f\u093f\u0915\u0932\u094d\u0938 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0906\u091c \u0906\u092a\u0915\u094b \u092f\u0939 \u0938\u092e\u091d\u093e\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u0906\u092a \u0915\u0948\u0938\u0947 \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u092c\u0939\u0941\u0924 \u0915\u092e \u0938\u092e\u092f \u092e\u0947\u0902 \u0938\u0939\u0940-\u0938\u0939\u0940 \u0938\u0949\u0932\u094d\u0935 \u0915\u0930 \u092a\u093e\u090f\u0902\u0917\u0947 \u0939\u092e \u0906\u092a\u0915\u094b \u092f\u0939 \u092c\u0924\u093e\u090f\u0902\u0917\u0947 \u0915\u093f \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948 \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u094b \u0915\u0948\u0938\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u0930\u0928\u093e \u0939\u0948 \u0924\u0925\u093e \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0915\u0948\u0938\u0947 \u0938\u092e\u091d\u0947\u0902\u0917\u0947 \u092f\u0939 \u0938\u0935\u093e\u0932 \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0938\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0906\u092a\u0915\u094b \u0907\u0938\u0947 \u0930\u093f\u0915\u094d\u0935\u0947\u0938\u094d\u091f \u0915\u0930\u0928\u093e \u0939\u0948 \u0906\u091c \u0939\u092e \u092c\u093e\u0924 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u0939\u0948\u0902<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-967 size-full\" src=\"https:\/\/www.reilsolar.com\/ebook\/wp-content\/uploads\/sites\/7\/2021\/07\/Tips-Tricks-and-Shortcuts-for-Solving-Linear-Equations-Questions.jpg\" alt=\"\" width=\"1280\" height=\"720\" srcset=\"https:\/\/www.reilsolar.com\/ebook\/wp-content\/uploads\/sites\/7\/2021\/07\/Tips-Tricks-and-Shortcuts-for-Solving-Linear-Equations-Questions.jpg 1280w, https:\/\/www.reilsolar.com\/ebook\/wp-content\/uploads\/sites\/7\/2021\/07\/Tips-Tricks-and-Shortcuts-for-Solving-Linear-Equations-Questions-300x169.jpg 300w, https:\/\/www.reilsolar.com\/ebook\/wp-content\/uploads\/sites\/7\/2021\/07\/Tips-Tricks-and-Shortcuts-for-Solving-Linear-Equations-Questions-1024x576.jpg 1024w, https:\/\/www.reilsolar.com\/ebook\/wp-content\/uploads\/sites\/7\/2021\/07\/Tips-Tricks-and-Shortcuts-for-Solving-Linear-Equations-Questions-768x432.jpg 768w\" sizes=\"auto, (max-width: 1280px) 100vw, 1280px\" \/><\/p>\n<h2>What is linear equation?<\/h2>\n<p style=\"text-align: center\">linear equation are those equation with degree of variable as one<\/p>\n<p style=\"text-align: center\">\u0930\u0948\u0916\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0935\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u093f\u0928\u092e\u0947\u0902 \u091a\u0930 \u0915\u0940 \u0918\u093e\u0924 \u090f\u0915 \u0939\u094b\u0924\u0940 \u0939\u0948<\/p>\n<h2>General form of linear equation<\/h2>\n<p style=\"text-align: center\"><strong>ax+b=0<\/strong><\/p>\n<p style=\"text-align: center\"><strong>ax+by+c=0<\/strong><\/p>\n<h2>Short Tricks Method of solving linear equation<\/h2>\n<p>The questions of Linear Equation can be asked mainly in two ways but at the same time, the questions of Linear Equation can also be easily solved in very less time with the help of Mental Calculation, we will tell you about the main two ways. Solve the questions of linear equation according to these maths but we will remember that you can solve such questions apart from these two.<\/p>\n<p>\u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u092e\u0941\u0916\u094d\u092f\u0924\u0903 \u0926\u094b \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u0938\u0935\u093e\u0932 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0932\u0947\u0915\u093f\u0928 \u0907\u0938\u0915\u0947 \u0938\u093e\u0925 \u0939\u0940 \u0938\u093e\u0925 \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u092e\u0947\u0902\u091f\u0932 \u0915\u0948\u0932\u0915\u0941\u0932\u0947\u0936\u0928 \u0915\u0947 \u092e\u0926\u0926 \u0938\u0947 \u092d\u0940 \u092c\u0939\u0941\u0924 \u0915\u092e \u0938\u092e\u092f \u092e\u0947\u0902 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0939\u092e \u0906\u092a\u0915\u094b \u092e\u0941\u0916\u094d\u092f \u0926\u094b \u0924\u0930\u0940\u0915\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u092c\u0924\u093e\u090f\u0902\u0917\u0947 \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0907\u0928 \u092e\u0948\u0925\u094d\u0938 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0938\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u0930 \u092a\u093e\u090f \u0932\u0947\u0915\u093f\u0928 \u0939\u092e \u0906\u092a\u0915\u094b \u092f\u093e\u0926 \u0906\u090f\u0902\u0917\u0947 \u0915\u093f \u0906\u092a \u0907\u0928 \u0926\u094b\u0928\u094b\u0902 \u0915\u0947 \u0905\u0932\u093e\u0935\u093e \u092d\u0940 \u0910\u0938\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0938\u0949\u0932\u094d\u0935 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902<\/p>\n<ol>\n<li>Elimination Method: One of the main method in solving the questions of linear equation is the elimination method in which we try to solve the questions by eliminating the variables prominently or noticeable whatever variables are there, you pay attention to those variables and see that That if any of those variables are being removed, it can be removed, then you should remove it as your variables will be less, you will be able to solve those questions very easily and in the elimination method, this is the main thing that has to be taken care of. that how you minimize the variable and if you take a single variable then surely if you get the answer for one variable then you will be able to find out the value of other also with their help. (\u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0938\u0949\u0932\u094d\u0935 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u090f\u0915 \u092a\u094d\u0930\u092e\u0941\u0916 \u0924\u0930\u0940\u0915\u093e \u0939\u0948 \u090f\u0932\u093f\u092e\u093f\u0928\u0947\u0936\u0928 \u092e\u0947\u0925\u0921 \u091c\u093f\u0938\u092e\u0947\u0902 \u0939\u092e \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u094b \u090f\u0932\u093f\u092e\u093f\u0928\u0947\u091f \u0915\u0930 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0938\u0949\u0932\u094d\u0935 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u092a\u094d\u0930\u092e\u0941\u0916 \u0930\u0942\u092a \u0938\u0947 \u092f\u093e \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u0947 \u092f\u094b\u0917\u094d\u092f \u0939\u0948 \u091c\u093f\u0924\u0928\u0940 \u092d\u0940 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0939\u0948\u0902 \u0906\u092a \u0909\u0928 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u094b \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0914\u0930 \u092f\u0939 \u0926\u0947\u0916\u0947\u0902 \u0915\u093f \u0909\u0928\u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u094b \u0905\u0917\u0930 \u0939\u091f\u093e\u092f\u093e \u091c\u093e \u0930\u0939\u093e \u0939\u0948 \u092f\u0939 \u0939\u091f\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u094b \u0924\u094b \u0906\u092a \u0909\u0938\u0947 \u0939\u091f\u093e \u0926\u0947\u0902 \u091c\u0948\u0938\u0947 \u0906\u092a\u0915\u0947 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u092e \u0939\u094b\u0902\u0917\u0947 \u0906\u092a \u0909\u0928 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u092c\u0939\u0941\u0924 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u0930 \u092a\u093e\u090f\u0902\u0917\u0947 \u0914\u0930 \u090f\u0932\u093f\u092e\u093f\u0928\u0947\u0936\u0928 \u092e\u0947\u0925\u0921 \u092e\u0947\u0902 \u0907\u0938\u0940 \u092c\u093e\u0924\u094b\u0902 \u0915\u093e \u092e\u0941\u0916\u094d\u092f \u0930\u0941\u092a \u0938\u0947 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f \u0906\u092a \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u094b \u0915\u0948\u0938\u0947 \u0915\u092e \u0938\u0947 \u0915\u092e \u0915\u0930\u0947\u0902 \u0914\u0930 \u0905\u0917\u0930 \u0906\u092a \u0938\u093f\u0902\u0917\u0932 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0932\u0947\u0924\u0947 \u0939\u0948\u0902 \u0924\u094b \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0906\u092a\u0915\u094b \u090f\u0915 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u0947 \u0905\u0917\u0930 \u0909\u0924\u094d\u0924\u0930 \u0906 \u0917\u090f \u0924\u094b \u0906\u092a \u0909\u0928\u0915\u0940 \u092e\u0926\u0926 \u0938\u0947 \u0926\u0942\u0938\u0930\u0947 \u092d\u0940 \u0935\u0948\u0932\u094d\u092f\u0942 \u092a\u0924\u093e \u0915\u0930 \u092a\u093e\u090f\u0902\u0917\u0947)<\/li>\n<li>Substitution Method: Linear Equation questions can be solved according to the substitution method if you have more variables and you are eliminating them then you should also pay attention to whether you will be able to solve it according to the sub tuition method Substitution Situation The main thing to note in this is that to find the value of one variable with the help of another variable and use that value force to say the other means that by using the equation you can find the value of any of its variables. And then try to solve that value by retrieving that value in another query so that you will use the value value of a variable. (\u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0938\u092c\u094d\u0938\u0940\u091f\u094d\u092f\u0942\u0936\u0928 \u092e\u0947\u0925\u0921 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0938\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0905\u0917\u0930 \u0906\u092a\u0915\u0947 \u092a\u093e\u0938 \u0905\u0927\u093f\u0915 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0939\u0948\u0902 \u0914\u0930 \u0906\u092a \u0909\u0938\u0947 \u090f\u0932\u093f\u092e\u093f\u0928\u0947\u091f \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902 \u0924\u092c \u0906\u092a\u0915\u094b \u092f\u0939 \u092d\u0940 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u093e \u091a\u093e\u0939\u093f\u090f \u0915\u093f \u0915\u094d\u092f\u093e \u0906\u092a \u0938\u092c \u091f\u094d\u092f\u0942\u0936\u0928 \u092e\u0947\u0925\u0921 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0938\u0947 \u0907\u0938\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u0930 \u092a\u093e\u090f\u0902\u0917\u0947 \u0938\u092c\u094d\u0938\u094d\u091f\u093f\u091f\u0942\u0936\u0928 \u092c\u0948\u0920\u0915 \u092e\u0947\u0902 \u092e\u0941\u0916\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u092f\u0939 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u093f\u0938\u0940 \u090f\u0915 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u0940 \u0935\u0948\u0932\u094d\u092f\u0942 \u0915\u094b \u092a\u0924\u093e \u0915\u0930\u0928\u093e \u0915\u093f\u0938\u0940 \u0926\u0942\u0938\u0930\u0947 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u0940 \u092e\u0926\u0926 \u0938\u0947 \u0914\u0930 \u0909\u0938 \u0935\u0948\u0932\u094d\u092f\u0942 \u092c\u0932 \u0915\u094b \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u0926\u0942\u0938\u0930\u0947 \u0915\u0947 \u0915\u0939\u0928\u0947 \u0915\u093e \u092e\u0924\u0932\u092c \u092f\u0939 \u0939\u0948 \u0915\u093f \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0906\u092a \u0909\u0938\u0915\u0947 \u0915\u093f\u0938\u0940 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u093e \u0935\u0948\u0932\u094d\u092f\u0942 \u0928\u093f\u0915\u093e\u0932\u0928\u0947 \u0914\u0930 \u092b\u093f\u0930 \u0909\u0938 \u0935\u0948\u0932\u094d\u092f\u0942 \u0915\u094b \u0926\u0942\u0938\u0930\u0947 \u0915\u094d\u0935\u0947\u0936\u094d\u091a\u0928 \u092e\u0947\u0902 \u092b\u0941\u091f\u0915\u0930 \u0909\u0938\u0940 \u0915\u094b \u0938\u0949\u0932\u094d\u0935 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0947\u0902 \u091c\u093f\u0938\u0938\u0947 \u0915\u093f \u0906\u092a\u0915\u094b \u0915\u093f\u0938\u0940 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0915\u0940 \u0935\u0948\u0932\u094d\u092f\u0942 \u0935\u0948\u0932\u094d\u092f\u0942 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947)<\/li>\n<\/ol>\n<h2>Conclusion for solving linear equation questions<\/h2>\n<p>Before serving the questions of Linear Equation, we have to note that we have given questions in government job or in your board examination or if you are studying in any class, then if you have to shame their questions.<\/p>\n<p>\u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0938\u0930\u094d\u0935 \u0915\u0930\u0928\u0947 \u0938\u0947 \u092a\u0939\u0932\u0947 \u0939\u092e\u0947\u0902 \u0905\u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u093e \u0939\u0948 \u0915\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0924\u094b \u0938\u0935\u093e\u0932 \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902 \u0938\u0930\u0915\u093e\u0930\u0940 \u0928\u094c\u0915\u0930\u0940 \u092e\u0947\u0902 \u092f\u093e \u0906\u092a\u0915\u0940 \u092c\u094b\u0930\u094d\u0921 \u090f\u0917\u094d\u091c\u093e\u092e\u093f\u0928\u0947\u0936\u0928 \u092e\u0947\u0902 \u092f\u093e \u092b\u093f\u0930 \u0906\u092a \u0915\u093f\u0938\u0940 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u092a\u0922\u093c\u093e\u0908 \u0915\u0930 \u0930\u0939\u0947 \u0939\u094b \u0924\u094b \u0909\u0928\u0915\u0947 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0905\u0917\u0930 \u0906\u092a\u0915\u094b \u0936\u0930\u094d\u092e \u0915\u0930\u0928\u093e \u0939\u0948<\/p>\n<p>In the questions, try to understand which variables are coming in whose values \u200b\u200bto find out and according to them you have to make equations which are linear equations and with the help of those linear equations then you have to solve those questions. It is mainly worth noting that in the questions you are reading or to pay attention to which variables are there and how will be able to make off linear equations from those variables whether they will take the question is the request or not all these Pay attention to things and then you have to design the linear equation, then solve it and solve the questions.<\/p>\n<p>\u0938\u0935\u093e\u0932\u094b\u0902 \u092e\u0947\u0902 \u092f\u0939 \u0938\u092e\u091d\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0928\u093e \u0939\u0948 \u0915\u093f\u0938 \u092e\u0947\u0902 \u0915\u094c\u0928-\u0915\u094c\u0928 \u0938\u0947 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0906 \u0930\u0939\u0947 \u0939\u0948\u0902 \u091c\u093f\u0928\u0915\u0947 \u0935\u0948\u0932\u094d\u092f\u0942 \u092a\u0924\u093e \u0915\u0930\u0928\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0938\u0947 \u0906\u092a\u0915\u094b \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u092c\u0928\u093e\u0928\u0947 \u0939\u0948\u0902 \u091c\u094b \u0915\u093f \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0939\u0948\u0902 \u0914\u0930 \u0909\u0928 \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u0947 \u092e\u0926\u0926 \u0938\u0947 \u092b\u093f\u0930 \u0906\u092a\u0915\u094b \u0909\u0928 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0938\u0949\u0932\u094d\u0935 \u0915\u0930\u0928\u093e \u0939\u0948 \u092e\u0941\u0916\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u092f\u0939 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u0947 \u092f\u094b\u0917\u094d\u092f \u0939\u0948 \u0915\u093f \u0906\u092a \u091c\u094b \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u092a\u0922\u093c \u0930\u0939\u0947 \u0939\u0948\u0902 \u0909\u0938\u092e\u0947\u0902 \u092f\u093e \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u093e \u0939\u0948 \u0915\u093f \u0915\u094c\u0928-\u0915\u094c\u0928 \u0938\u0940 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0939\u0948\u0902 \u0914\u0930 \u0909\u0928 \u0935\u0947\u0930\u093f\u090f\u092c\u0932 \u0938\u0947 \u0915\u0948\u0938\u0947 \u0911\u092b \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u092c\u0928\u093e \u092a\u093e\u090f\u0902\u0917\u0947 \u0915\u094d\u092f\u093e \u0935\u0939 \u0938\u0935\u093e\u0932 \u0932\u0947\u0902\u0917\u0947 \u0930\u093f\u0915\u094d\u0935\u0947\u0938\u094d\u091f \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902 \u0939\u0948 \u0907\u0928 \u0938\u092d\u0940 \u091a\u0940\u091c\u094b\u0902 \u0915\u094b \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0928\u093e \u0914\u0930 \u092b\u093f\u0930 \u0906\u092a\u0915\u094b \u0932\u0940\u0928\u093f\u092f\u0930 \u0907\u0915\u094d\u0935\u0947\u0936\u0928 \u0915\u093e \u0921\u093f\u091c\u093e\u0907\u0928 \u0915\u0930\u0928\u093e \u0939\u0948 \u092b\u093f\u0930 \u0909\u0938\u0947 \u0938\u0949\u0932\u094d\u0935 \u0915\u0930 \u0938\u0935\u093e\u0932\u094b\u0902 \u0915\u094b \u0938\u0949\u0932\u094d\u0935 \u0915\u0930\u0928\u093e \u0939\u0948<\/p>\n<p class=\"\" data-start=\"0\" data-end=\"196\">Here\u2019s a complete guide on <strong data-start=\"27\" data-end=\"76\">Linear Equations: Tips, Tricks, and Shortcuts<\/strong> to help you solve problems faster\u2014ideal for <strong data-start=\"121\" data-end=\"142\">competitive exams<\/strong> like SSC, TNPSC, RRB, Banking, NEET, or school tests.<\/p>\n<h3 data-start=\"203\" data-end=\"239\"><strong data-start=\"209\" data-end=\"239\">What is a Linear Equation?<\/strong><\/h3>\n<p class=\"\" data-start=\"240\" data-end=\"264\">An equation of the form:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">ax+b=0ax + b = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/p>\n<p class=\"\" data-start=\"284\" data-end=\"290\">Where:<\/p>\n<ul data-start=\"291\" data-end=\"388\">\n<li class=\"\" data-start=\"291\" data-end=\"317\">\n<p class=\"\" data-start=\"293\" data-end=\"317\"><code data-start=\"293\" data-end=\"296\">a<\/code>, <code data-start=\"298\" data-end=\"301\">b<\/code> are constants<\/p>\n<\/li>\n<li class=\"\" data-start=\"318\" data-end=\"341\">\n<p class=\"\" data-start=\"320\" data-end=\"341\"><code data-start=\"320\" data-end=\"323\">x<\/code> is the variable<\/p>\n<\/li>\n<li class=\"\" data-start=\"342\" data-end=\"388\">\n<p class=\"\" data-start=\"344\" data-end=\"388\">Degree of the equation = 1 (hence, <em data-start=\"379\" data-end=\"387\">linear<\/em>)<\/p>\n<\/li>\n<\/ul>\n<h3 data-start=\"395\" data-end=\"437\"><strong data-start=\"401\" data-end=\"437\">Basic Types of Linear Equations:<\/strong><\/h3>\n<ol data-start=\"438\" data-end=\"641\">\n<li class=\"\" data-start=\"438\" data-end=\"483\">\n<p class=\"\" data-start=\"441\" data-end=\"483\"><strong data-start=\"441\" data-end=\"460\">In one variable<\/strong> \u2013 e.g., <code data-start=\"469\" data-end=\"481\">2x - 5 = 7<\/code><\/p>\n<\/li>\n<li class=\"\" data-start=\"484\" data-end=\"532\">\n<p class=\"\" data-start=\"487\" data-end=\"532\"><strong data-start=\"487\" data-end=\"507\">In two variables<\/strong> \u2013 e.g., <code data-start=\"516\" data-end=\"530\">3x + 2y = 12<\/code><\/p>\n<\/li>\n<li class=\"\" data-start=\"533\" data-end=\"641\">\n<p class=\"\" data-start=\"536\" data-end=\"580\"><strong data-start=\"536\" data-end=\"564\">Pair of linear equations<\/strong> \u2013 solved using:<\/p>\n<ul data-start=\"584\" data-end=\"641\">\n<li class=\"\" data-start=\"584\" data-end=\"598\">\n<p class=\"\" data-start=\"586\" data-end=\"598\">Substitution<\/p>\n<\/li>\n<li class=\"\" data-start=\"602\" data-end=\"615\">\n<p class=\"\" data-start=\"604\" data-end=\"615\">Elimination<\/p>\n<\/li>\n<li class=\"\" data-start=\"619\" data-end=\"641\">\n<p class=\"\" data-start=\"621\" data-end=\"641\">Cross multiplication<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h3 data-start=\"648\" data-end=\"686\"><strong data-start=\"654\" data-end=\"686\">Tips &amp; Tricks to Solve Fast:<\/strong><\/h3>\n<h3 class=\"\" data-start=\"688\" data-end=\"743\">\u00a01. <strong data-start=\"698\" data-end=\"743\">Cross Multiplication Method (2 Variables)<\/strong><\/h3>\n<p class=\"\" data-start=\"744\" data-end=\"758\">For equations:<\/p>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\"><span class=\"hljs-attribute\">a1x<\/span> + b1y = c1<br \/>\na2x + b2y = c2<br \/>\n<\/code><\/div>\n<\/div>\n<p class=\"\" data-start=\"801\" data-end=\"805\">Use:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">x=(b1\u00d7c2\u2212b2\u00d7c1)(a1\u00d7b2\u2212a2\u00d7b1),y=(c1\u00d7a2\u2212c2\u00d7a1)(a1\u00d7b2\u2212a2\u00d7b1)x = \\frac{(b1\u00d7c2 &#8211; b2\u00d7c1)}{(a1\u00d7b2 &#8211; a2\u00d7b1)}, \\quad y = \\frac{(c1\u00d7a2 &#8211; c2\u00d7a1)}{(a1\u00d7b2 &#8211; a2\u00d7b1)}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span>1<span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">b<\/span>2<span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">a<\/span>2<span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">b<\/span>1<span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span>1<span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">c<\/span>2<span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">b<\/span>2<span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">c<\/span>1<span class=\"mclose\">)<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span>1<span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">b<\/span>2<span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">a<\/span>2<span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">b<\/span>1<span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">c<\/span>1<span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">a<\/span>2<span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">c<\/span>2<span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">a<\/span>1<span class=\"mclose\">)<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p class=\"\" data-start=\"909\" data-end=\"961\">\u00a0Quickest method in exams \u2013 no need to substitute!<\/p>\n<h3 class=\"\" data-start=\"968\" data-end=\"1002\">\u00a02. <strong data-start=\"978\" data-end=\"1002\">Elimination Shortcut<\/strong><\/h3>\n<p class=\"\" data-start=\"1003\" data-end=\"1051\">Make coefficients same \u2192 add\/subtract equations:<\/p>\n<p class=\"\" data-start=\"1053\" data-end=\"1061\">Example:<\/p>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\">2x + 3y = 12<br \/>\n4x + 3y = 18<br \/>\n<\/code><\/div>\n<\/div>\n<p class=\"\" data-start=\"1100\" data-end=\"1119\">Subtract equations:<\/p>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\">(<span class=\"hljs-number\">4<\/span>x - <span class=\"hljs-number\">2<\/span>x) = (<span class=\"hljs-number\">18<\/span> - <span class=\"hljs-number\">12<\/span>) \u2192 <span class=\"hljs-number\">2<\/span>x = <span class=\"hljs-number\">6<\/span> \u2192 x = <span class=\"hljs-number\">3<\/span><br \/>\n<span class=\"hljs-keyword\">Then<\/span> plug <span class=\"hljs-keyword\">in<\/span> x <span class=\"hljs-keyword\">to<\/span> <span class=\"hljs-keyword\">get<\/span> y.<br \/>\n<\/code><\/div>\n<\/div>\n<h3 class=\"\" data-start=\"1200\" data-end=\"1249\">\u00a03. <strong data-start=\"1210\" data-end=\"1249\">Zero Trick (For Plugging in values)<\/strong><\/h3>\n<p class=\"\" data-start=\"1250\" data-end=\"1346\">Some MCQs allow <strong data-start=\"1266\" data-end=\"1283\">trial &amp; error<\/strong>. Put options into the equation to see which satisfies fastest.<\/p>\n<h3 class=\"\" data-start=\"1353\" data-end=\"1395\">\u00a04. <strong data-start=\"1363\" data-end=\"1395\">Shortcut for Equations like:<\/strong><\/h3>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">x+yx\u2212y=aandx\u2212yx+y=b\\frac{x + y}{x &#8211; y} = a \\quad \\text{and} \\quad \\frac{x &#8211; y}{x + y} = b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><span class=\"mord mathnormal\">y<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord text\"><span class=\"mord\">and<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">y<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span><\/p>\n<p class=\"\" data-start=\"1474\" data-end=\"1495\">Multiply both to get:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(x+yx\u2212y)\u00d7(x\u2212yx+y)=ab\u21921=ab\u2192a=1\/b\\left(\\frac{x + y}{x &#8211; y}\\right) \u00d7 \\left(\\frac{x &#8211; y}{x + y}\\right) = ab \u2192 1 = ab \u2192 a = 1\/b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><span class=\"mord mathnormal\">y<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"minner\"><span class=\"mopen delimcenter\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">y<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">ab<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">ab<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1\/<\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"\" data-start=\"1600\" data-end=\"1639\">\u00a05. <strong data-start=\"1610\" data-end=\"1639\">Equations with Fractions:<\/strong><\/h3>\n<p class=\"\" data-start=\"1640\" data-end=\"1679\">Clear denominators by taking LCM early:<\/p>\n<p><span class=\"katex-error\" title=\"ParseError: KaTeX parse error: Expected 'EOF', got '&amp;' at position 44: \u20265  \n\u2192 LCM of 2 &amp;\u0332 3 = 6  \n\u2192 Mult\u2026\">\\frac{x}{2} + \\frac{x}{3} = 5 \u2192 LCM of 2 &amp; 3 = 6 \u2192 Multiply entire equation by 6: 3x + 2x = 30 \u2192 5x = 30 \u2192 x = 6<\/span><\/p>\n<h3 data-start=\"1810\" data-end=\"1851\"><strong data-start=\"1816\" data-end=\"1851\">Mental Tricks for Common Forms:<\/strong><\/h3>\n<div class=\"overflow-x-auto contain-inline-size\">\n<table data-start=\"1853\" data-end=\"2082\">\n<thead data-start=\"1853\" data-end=\"1884\">\n<tr data-start=\"1853\" data-end=\"1884\">\n<th data-start=\"1853\" data-end=\"1860\">Form<\/th>\n<th data-start=\"1860\" data-end=\"1884\">Shortcut\/Observation<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1917\" data-end=\"2082\">\n<tr data-start=\"1917\" data-end=\"1958\">\n<td><code data-start=\"1919\" data-end=\"1931\">ax + b = 0<\/code><\/td>\n<td><span class=\"katex\"><span class=\"katex-mathml\">x=\u2212bax = \\frac{-b}{a}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2212<span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr data-start=\"1959\" data-end=\"2041\">\n<td><code data-start=\"1961\" data-end=\"1972\">x + y = a<\/code> and <code data-start=\"1977\" data-end=\"1988\">x - y = b<\/code><\/td>\n<td><span class=\"katex\"><span class=\"katex-mathml\">x=a+b2,\u00a0y=a\u2212b2x = \\frac{a + b}{2}, \\ y = \\frac{a &#8211; b}{2}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">a<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr data-start=\"2042\" data-end=\"2082\">\n<td><code data-start=\"2044\" data-end=\"2056\">x = a \u00b1 \u221ab<\/code><\/td>\n<td>Think quadratic roots<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3 data-start=\"2089\" data-end=\"2122\"><strong data-start=\"2095\" data-end=\"2122\">Quick Practice Example:<\/strong><\/h3>\n<h3 class=\"\" data-start=\"2124\" data-end=\"2138\">Q: Solve<\/h3>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary\">\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\">3x + 2y = 12<br \/>\n2x + 3y = 13<br \/>\n<\/code><\/div>\n<\/div>\n<p class=\"\" data-start=\"2178\" data-end=\"2201\"><strong data-start=\"2178\" data-end=\"2201\">Elimination Method:<\/strong><\/p>\n<p class=\"\" data-start=\"2203\" data-end=\"2368\">Multiply first by 3: <code data-start=\"2224\" data-end=\"2238\">9x + 6y = 36<\/code><br data-start=\"2238\" data-end=\"2241\" \/>Multiply second by 2: <code data-start=\"2263\" data-end=\"2277\">4x + 6y = 26<\/code><br data-start=\"2277\" data-end=\"2280\" \/>Subtract: <code data-start=\"2290\" data-end=\"2307\">5x = 10 \u2192 x = 2<\/code><br data-start=\"2307\" data-end=\"2310\" \/>Put x = 2 in first: <code data-start=\"2330\" data-end=\"2368\">3(2) + 2y = 12 \u2192 6 + 2y = 12 \u2192 y = 3<\/code><\/p>\n<p class=\"\" data-start=\"2370\" data-end=\"2396\">\u00a0Answer: <strong data-start=\"2380\" data-end=\"2396\">x = 2, y = 3<\/strong><\/p>\n<h3 data-start=\"2403\" data-end=\"2457\">\u00a0Want a PDF with Practice Questions + Answer Key?<\/h3>\n<p class=\"\" data-start=\"2459\" data-end=\"2483\">I can generate one with:<\/p>\n<ul data-start=\"2484\" data-end=\"2567\">\n<li class=\"\" data-start=\"2484\" data-end=\"2498\">\n<p class=\"\" data-start=\"2486\" data-end=\"2498\">10\u201315 MCQs<\/p>\n<\/li>\n<li class=\"\" data-start=\"2499\" data-end=\"2532\">\n<p class=\"\" data-start=\"2501\" data-end=\"2532\">Fast solving tricks explained<\/p>\n<\/li>\n<li class=\"\" data-start=\"2533\" data-end=\"2567\">\n<p class=\"\" data-start=\"2535\" data-end=\"2567\">Practice problems with solutions<\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"2569\" data-end=\"2622\">Want that? Or prefer a <strong data-start=\"2592\" data-end=\"2608\">visual chart<\/strong> for revision?<\/p>\n<h3 data-start=\"2569\" data-end=\"2622\"><a href=\"https:\/\/www.jaipuria.ac.in\/blog\/wp-content\/uploads\/2023\/07\/Quant-Short-Tricks-PDF.pdf\" target=\"_blank\" rel=\"noopener\">LINEAR EQUATIONS : Tips, Tricks and Shortcuts for Solving Questions<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.sac.edu\/StudentServices\/EOPS\/Documents\/Math%20Study%20Guide%207%20-%20Solving%20Linear%20Equations.pdf\" target=\"_blank\" rel=\"noopener\">Math Study Guide 7 &#8211; Solving Linear Equations.pdf<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.pearsonhighered.com\/assets\/samplechapter\/0\/3\/2\/1\/0321947622.pdf\" target=\"_blank\" rel=\"noopener\">Systems of Linear Equations; Matrices<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Questions of Linear Equation can be solved very easily through short trick shot techniques, we will try to explain to you today through our articles that how you can solve the questions of Linear Equation correctly in very less time. We will tell you what is linear equation, how to solve linear equation and how [&hellip;]<\/p>\n","protected":false},"author":12,"featured_media":967,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[34],"tags":[39],"class_list":["post-966","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-tricks-pdf","tag-linear-equation-tricks"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/posts\/966","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/comments?post=966"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/posts\/966\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/media\/967"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/media?parent=966"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/categories?post=966"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/ebook\/wp-json\/wp\/v2\/tags?post=966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}