Begin by letting the unknowns in the two boxes be x and y.

FIll in the information you know about the inputs and outputs.

ocr-gcse-tq-ma-functions-hard-q3-diagram-1

Use the information to form equations.

Number the equations so that they are easier to solve.

$3 x - y = 5 (1) 7 x - y = 25 (2)$

[1]

Eliminate the y terms by subtracting equation (1) from equation (2). Be careful to subtract every term.
The coefficients of y are the same with the same signs, so subtract them.

$7 x - y = 25 - (3 x - y = 5) 4 x = 20$

[1]

Solve the equation to find x by dividing both sides by 4.

$\begin{array}{rcl} x & = & \frac{20}{4} = 5 \end{array}$

Substitute $x = 5$ into either of the two original equations.

$(1) 3 (5) - y = 5$

Solve this equation to find y.

$\begin{array}{rcl} 15 - y & = & 5 \\ y & = & 10 \end{array}$

Substitute $x = 5$ and $y = 10$ into the other equation to check that they are correct.

$\begin{array}{rcl} (2) 7 x - y & = & 25 \\ 7 (5) - 10 & = & 25 \\ 35 - 10 & = & 25 \\ 25 & = & 25 \end{array}$

34U_8gdZ_ocr-gcse-tq-ma-functions-hard-q3-diagram-2 [1]

Input	Output
$8$	$2$
$12$	$3$
$20$	...............
...............	$9$

Input	Output
$2$	$28$
$4$	$36$
$7$	...............
...............	$72$

Functions (Edexcel GCSE Maths: Foundation)

Exam Questions