# Elimination Method of Simultaneous Equations

Published on ginnyent on 9th April, 2019
Example 1
Solve simultaneously by elimination
2x + 4y = 42
6x – 4y = 30 (Culled from Comprehensive Maths).

Solution
Let the equations be equation 1 and 2 respectively.
2x + 4y = 42 ———-1
6x – 4y = 30———-2

If you look at the two equations very well, you will notice that the coefficient of y is the same in the two equations; 4 is the coefficient.

In order to eliminate y, add equation 1 and 2

So we have:
2x + 6x + 4y -4y = 42 +30
So we have: 8x = 72
x = 72/8
x = 9.

Now that we know the value of x, let’s find y.
We can use either of the two equations to find y.
2x + 4y = 42
2(9) + 4y = 42
18 + 4y = 42
4y = 42 – 18
4y = 24
y = 24/4
y = 6.

Example 2
Solve by elimination method:
4x +5y = 23
4x – y = 5

Solution
Call the equations 1 and 2 respectively.
4x +5y = 23——1
4x – y = 5———-2
If you look at the equations very well, you would see that x has the same coefficient in the two equations. So we will eliminate x.
To eliminate x, subtract equation 2 from 1.
(Do you know why we are subtracting?)

So we have:
4x – 4x+5y- (-y) = 23 – 5
5y + y = 18 (Understood?)
6y = 18
y = 18/6
y = 3

Now that we have found y, let’s find x using equation 1 or 2.
In equation 2, 4x – y = 5
4x – 3 = 5
4x = 5 + 3 (Understood?)
4x = 8
x = 8/4
x = 2.

Exercise
Solve the following pairs of equations simultaneously by elimination method.

1. 3x + 2y = 13

x + 2y = 7

1. 5x -3y = 5

5x – 2y = 10

1. 6x + 5y = 11

6x – 5y = 1