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Simultaneous equations – practice for Year 9

Sample questions on Simultaneous equations with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Year 9
Curriculum area
Number and algebra

Question types: Two equations in two unknowns

Rule: Simultaneous equations

Elimination: add (or subtract) the equations so that one unknown disappears.

Substitution: express one unknown from one equation and put it into the other.

Example: x + y = 16, x − y = 4: adding them gives 2x = 20, x = 10, y = 6

Watch out: The question asks about one unknown: answer with the one it asks for (x or y).

Sample questions

  1. Question 1 Easy

    Solve the simultaneous equations: x + y = 22; x − y = 8. Find x.

    Show the solution
    Answer: 15

    How it works: Adding the equations: 2x = 30, x = 15; y = 22 − 15 = 7

  2. Question 2 Normal

    Solve the simultaneous equations: 3x + 3y = 30; −4x + y = −35. Find y.

    Show the solution
    Answer: 1

    How it works: x = 9, y = 1 (check: 3 × 9 + 3 × 1 = 30; (−4) × 9 + 1 × 1 = −35)

  3. Question 3 Hard

    A museum ticket costs £8 for an adult and £5 for a child. A group of 14 people paid £91 altogether. How many children were in the group?

    Show the solution
    Answer: 7

    How it works: If everyone were an adult, they would pay 14 × 8 = 112; the difference 21 ÷ 3 = 7 children

Related topics

All Maths topics

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