Solve Simultaneous Equations by Eliminating One Variable

In this activity, we need to try to eliminate one of the letters to solve the simultaneous equations.

 

Example

2x + 3y = 21

4x - 3y = 15

 

Method

First, look for the same number of x's or y's in both equations, in this case 3y.

If they have different signs, we add the two equations and are left with just x's.

 

2x + 3y = 21 (1)

4x - 3y = 15 (2)

 

Adding (1) and (2)

 

6x = 36

x = 36 ÷ 6

x = 6

 

When we know one value, in this case x = 6, we substitute in one equation to find the other.

Substituting x = 6 into (1)

 

2x + 3y = 21

2 x 6 + 3y = 21

12 + 3y = 21

3y = 21 - 12

3y = 9

y = 9 ÷ 3

y = 3

 

We can check the answer by substituting both values into the other equation:

4 × 6 - 3 × 3 = 24 - 9 = 15 correct.

SOLUTION: x = 6 and y = 3

 

Example 2

7x - 4y = 27 (1)

4x - 4y = 12 (2)

 

As both coefficients of y are the same, we subtract.

 

(1) - (2)

 

3x = 15

x = 5

 

Substituting in  x = 5 into equation (1)

 

7 × 5 - 4y = 27

35 - 4y = 27

- 4y = -8

y = 2

Checking in (2) 4 × 5 - 4 × 2 = 20 - 8 = 12 correct.

SOLUTION: x = 5 and y = 2