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## Elimination Method To Solve System Of Linear Equations

The method of elimination is most often used by students to solve a system of linear equations. Moreover, this method is easy to understand and involves the addition and subtraction of polynomials. Students should be able to add and subtract polynomials involving two or three variables.

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

**2x – 5a = 11**

**3x + 2a = 7**

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

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

**(2x – 5a = 11) * 3**

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

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

**6x – 15y = 33**

**6x + 4a = 14**

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

**(6x – 15y = 33) – (6x + 4y = 14)**

In the next step, combine similar terms:

**6x – 6x – 15y – 4y = 33 – 14**

**– 19a = 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 equations given in the question.

Substitute the value of “y = – 1” in the 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**

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

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