The elimination method is one of the methods to solve pair of simultaneous linear equations. By applying arithmetic properties, we reduce one of the equations that has only one variable and determine the another one. This section will help you to understand how to use elimination method to solve linear equations with two variables in a simple way.

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We always emphasize on how important a role math can play in your brain development. Those students are preparing for competitive exams that require mathematical skills and reasoning skills. A lot of students openly admit they are weak at math and just wanted to clear the school exam and nothing more. There are a lot of factors that can anxiety in kids and make them scared of studies. We help students overcome math anxiety and get better at studies. We believe that students can score more when they get help before it was too late to correct their mistakes. Also we provide NCERT Solutions involve detailed solutions of all linear equations questions. Thorough solutions to the questions provided with the aim of helping students compare their answers and excel their skills.

A method can be used to solve the pair of linear equations with two variables having degree one. This method is known as the “Gaussian elimination method."

In the elimination method, the very first step is to obtain an equation in one variable either by adding or subtracting the equations. If again variables are not eliminated, we multiply one or both of the equations with a coefficients to get an equivalent linear system. Now it is easy to eliminate one of the variables.

### How to solve Linear Equations by Elimination

While solving Linear equations of two variables by the method of elimination, we follow the following steps.

Step 1

y - 4x = 3 .....(2)

-2(y - 4x = 3)

New equations are:

-3x + 2y = 4 and

8x - 2y = -6

Add these equations to eliminate y:

This implies, 5x = -2

x = -2/5

Plug it back the value of x in any of the given equations to solve for y.

By substituting the value of x, we get

2y - 3(-2/5) = 4

2y + 6/5 = 4

y = 7/5

x + 3y = 10; x + 2y = -5

x + 3y = 10 equation (1)

x + 2y = -5 equation (2)

Since the coefficient of x is same for the both the equations. Subtract equation 2 form equation 1,

So y = 15

Now solve for x:

Substitute 15 for y in x + 3y = 10

x + (3)(15) = 10

x + 45 = 10

x + 45 + (-45) = 10 + (-45) (Add -45 to both sides)

x = -35

3x + 7y = 1 and x - 2y = 4