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

$y = 2x - 3$ $x + y = 9$
Level 3 · 3 marksTry it
2
Solve the simultaneous equations

$y = x + 4$ $3x + y = 16$
Level 3 · 3 marksTry it
3
Solve the simultaneous equations

$y = 2x - 3$ $3x + 2y = 15$

(3 marks)
Level 3 · 3 marksTry it
4
$3$ pens and $2$ rulers cost £ $3.55$

$5$ pens and $4$ rulers cost £ $6.35$

Work out the cost of one pen and the cost of one ruler. Give your answers in pence. (3 marks)
Level 3 · 3 marksTry it
5
$3$ coffees and $2$ teas cost £ $10.10$ $2$ coffees and $5$ teas cost £ $12.05$

Work out the cost of one coffee and the cost of one tea. [4]
Level 3 · 4 marksTry it