GCSE · Simultaneous equations

Substitution and real-world simultaneous equationsExam-style questions

Why substitution collapses two equations into one, the bracket that guards every substitution, and how to translate two-fact word problems (prices, sums, perimeters, intersections) into a solvable pair.

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18 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Solve the simultaneous equations

$y = 3x + 1$ $2x + 3y = 25$
Level 4 · 3 marksTry it
2
Two numbers have a sum of 41 and a difference of 9.

Find the two numbers.
Level 4 · 3 marksTry it
3
The length of a rectangle is 3 cm more than twice its width.

The perimeter of the rectangle is 24 cm.

(a) Find the length and the width of the rectangle.

(b) Work out the area of the rectangle.
Level 4 · 4 marksTry it
4
Solve the simultaneous equations

$y = 2x + 1$ $5x - 2y = 8$
Level 4 · 3 marksTry it
5
Two numbers have a sum of $52$ .

One number is three times the other.

Find the two numbers.
Level 4 · 3 marksTry it

2 more questions on substitution and real-world simultaneous equations

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