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## Elimination Method To Solve System Of Linear Equations

The elimination method is most commonly used by students to solve systems of linear equations. Also, this method is easy to understand and involves adding and subtracting polynomials. Students must know how to add and subtract polynomials involving two or three variables.

In the elimination method, the coefficients of the same variable are made equal and then the two equations are subtracted to eliminate that 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 – 5y = 11**

**3x + 2y = 7**

To solve the above equation using the method of elimination, we need to make the coefficients of one of the variables (either “x” or “y”) equal by multiplying the equation by some numbers, and these numbers can be obtained finding the least common multiple of the coefficients. Consider that we want to make the coefficients of “x” equal 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 variable “x” in the equations, we need to multiply the first equation by “3” and the second by “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 the same coefficient of the variable “x” in both equations. Once one variable has the same coefficient, subtract one equation from the other. We subtract the second equation from the first as shown below:

**(6x – 15y = 33) – (6x + 4y = 14)**

In the next step combine the similar terms:

**6x – 6x – 15y – 4y = 33 – 14**

**– 19y = 19**

**y = -1**

So far, we have solved equations in 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” into 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**

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

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