# How to Solve Linear Equation by Elimination Method

## How to Solve Linear Equation by Elimination Method

##### Example 1:

Resolve the equations 3x - 5y = -16 and 2x + 5y = 31 and calculate the x and y value.

##### Given,

3x - 5y = -16 ---------- (1) 2x + 5y = 31 ---------- (2)

x and y value

##### Solution:

Let us calculate the value of x and y for the given linear equations using elimination method.

###### Step 1:

In the two equations coefficients of 'y' in both the equations are numerically equal. So, elimination of 'y' can be done easily. Now, add both the equation.

 3x - 5y = -16 ----- (1) 2x + 5y = 31 ----- (2) (1) + (2) 5x = 15

Therefore, x=15/5 = 3

###### Step 2:

Substitute the value x = 3 in any one of the equation. Let us substitute the x value in the 1st equation, 3x - 5y = -16.

 3x - 5y = -16 3(3)-5y = -16 9-5y = -16 -5y = -16-9 -5y = -25 y = 25/5 y = 5
Therefore the solution is (x,y) = (3,5)

##### Example 2:

Resolve the equations 6x + 4y = 6 and 7x - 8y = 10 and calculate the x and y value.

##### Given,

6x + 4y = 6 ---------- (1) 7x - 8y = 10 ---------- (2)

x and y value

##### Solution:

Let us calculate the value of x and y for the given linear equations using elimination method.

###### Step 1:

In the given two equations Coefficients of 'x' and 'y' are numerically different. So, in-order to make the co-efficients equal, let us multiply the first equation by 2 If the first equation is multiply by 2 , then coefficient of y is equal numerically.

 (1) * 2 12x +8y = 12 ----- (3) 7x - 8y = 10 ----- (2) (3) + (2) 19x = 22

Therefore, x = 22/19 = 1.158

###### Step 2:

Substitute the value x = 1.158 in (1) equation. 6x + 4y = 6 ---------- (1)

 6(1.158) + 4y = 6 6.948 + 4y = 6 4y = 6-6.948 4y = -0.948 y = -0.948/4 y = -0.237

Therefore the solution is (x,y) = (1.158,-0.237)