Method 1

Make the x terms equal by multiplying both sides of the first equation by 5 and both sides of the second equation by 2

$\begin{array}{rcl} 10 x + 15 y & = & - 60 \\ 10 x + 4 y & = & 28 \end{array}$

[1]

Subtract the second equation from the first (by subtracting each of the like terms individually, including the numbers on the right-hand side)
The x terms will disappear

$\begin{array}{rcl} 11 y & = & - 60 - 28 \\ 11 y & = & - 88 \end{array}$

[1]

Solve the remaining equation to find y (by dividing both sides by 11)

$\begin{array}{rcl} y & = & \frac{- 88}{11} \\ y & = & - 8 \end{array}$

[1]

The value of x is still required
Substitute y = -8 into either of the two original equations, for example 2x + 3y = -12

$2 x + 3 \times (- 8) = - 12$

Solve this equation to find x

$\begin{array}{rcl} 2 x - 24 & = & - 12 \\ 2 x & = & - 12 + 24 \\ 2 x & = & 12 \\ x & = & \frac{12}{2} \\ x & = & 6 \end{array}$

Check with a calculator that x = 6 and y = -8 satisfy the other original equation, 5x + 2y = 14

$\begin{array}{rcl} 5 \times 6 + 2 \times (- 8) & = & 14 \\ 30 - 16 & = & 14 \end{array}$

This is true, so both solutions are correct
Present both solutions together

$x = 6, y = - 8$ [1]

Pattern number	1	2	3	4
Number of grey mats	6	9	12	15
Total number of mats	6	10	15	21

Simultaneous Equations (Cambridge O Level Maths)

Exam Questions