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- Elimination Method To Solve System Of Linear Equations
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## Elimination Method To Solve System Of Linear Equations

Elimination method is used most frequently by the students to solve system of linear equations. Also, this method is easy to understand and involve adding and subtracting the polynomials. Students should know how to add and subtract polynomials involving two or three variables.

In elimination method, the coefficients of the same variable are made same and then both the equation are subtracted to eliminate that variable. The resultant equation involves only one variable and can be simplified easily. For example; consider there are two equations in the system of linear equations with variables “x” and “y” as shown below:

**2x – 5y = 11**

**3x + 2y = 7**

To solve above equation by elimination method, we have to make the coefficients of one of the variables (either “x” or “y”) same by multiplying the equation with some numbers, and these number can be obtained by finding the least common multiple of the coefficients. Consider we want to make coefficients of “x” same in both the equations. For that we have to find the least common multiple of “2” and “3” which is “6”.

To get “6” as the coefficient of both the “x” variable in equations we have to multiply the first equation with “3” and second equation with “2” as shown below:

**(2x – 5y = 11) * 3**

**(3x + 2y = 7) * 2**

The new set of equations after multiplication is obtained as shown below:

**6x – 15y = 33**

**6x + 4y = 14**

Now we have same coefficient of variable “x” in both the equations. Once the one variable got the same coefficient, subtract one equation from the other. We will subtract the second equation from the first one as shown below:

**(6x – 15y = 33) – (6x + 4y = 14)**

In the next step combine the like terms:

**6x – 6x – 15y – 4y = 33 – 14**

**– 19y = 19**

**y = – 1**

So far, we have solved the equations for one variable. To find the value of the other variable “x” we will substitute the value of “y” into one of the given equations in the question.

Substitute the value of “y = – 1” in equation 2x – 5y = 11 to find the value of “x” as shown in the next step:

**2x – 5 (- 1) = 11**

**2x + 5 = 11**

**2x = 11 – 5**

**2x = 6**

**x = 3**

Hence, we have solved both the equations to find the value of variables and our solution is x = 3 and y = – 1. You can adopt the same approach to solve the system of linear equations by eliminating one of the variables.

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