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

(Do you know why we added instead of subtracting?)

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.

- 3x + 2y = 13

x + 2y = 7

- 5x -3y = 5

5x – 2y = 10

- 6x + 5y = 11

6x – 5y = 1

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CHG Ofokansi is an author, medical laboratory scientist, a teacher who has several books for children and adults.
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