AQA · Mathematics · 8300

GCSE Maths: Simultaneous Equations (3 Unknowns)

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Simultaneous Equations (3 Unknowns) (Corbettmaths Video 393), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.

12 flashcards · Free to study · No account needed

Study this deck

Preparing your cards…

All questions and answers

Read through the full deck, or practise recalling each answer above.

  1. How do you solve three simultaneous equations in three unknowns by elimination?

    Show answer

    Eliminate the same variable from two different pairs of equations to get two equations in two unknowns, solve those, then substitute back to find the third.

  2. Solve: 2x + 3y + 5z = 21, 3x + 6y + 15z = 51, 5x + 4y + 10z = 37.

    Show answer

    x = 1, y = 3, z = 2.

  3. Solve: 2x + 4y − z = 15, 3x + 8y + z = 44, x + 2y + 2z = 15.

    Show answer

    x = −5, y = 7, z = 3.

  4. Solve: 7x + 5y + 4z = 23, 21x − 10y + 6z = −4, 7x + 15y − 2z = −15.

    Show answer

    x = −2, y = 1, z = 8.

  5. 12 cars, 6 motorcycles and 3 vans earn £1590 commission. Why is 4x + 2y + z = 530?

    Show answer

    The sales give 12x + 6y + 3z = 1590; dividing every term by 3 gives 4x + 2y + z = 530.

  6. Solve 4x + 2y + z = 530, 2x + y + z = 320, 9x + 2y + 3z = 1175 (Roshan's commissions).

    Show answer

    Car x = £85, motorcycle y = £40, van z = £110.

  7. Tickets were £25 cheaper last year; 4 adult, 8 child, 4 pensioner cost £6600. Derive x + 2y + z = 1750.

    Show answer

    4(x − 25) + 8(y − 25) + 4(z − 25) = 6600 gives 4x + 8y + 4z = 7000; divide by 4.

  8. Solve 2x + 3y + z = 2825, x − y − z = 50, x + 2y + z = 1750 (season tickets).

    Show answer

    Adult x = £725, child y = £350, pensioner z = £325.

  9. An ultra run that is 40% longer than a long run of z km has length ? km.

    Show answer

    1.4z

  10. Solve 4x + 3y + z = 75, x + 3y + 4z = 123, 7x + 2y + 7z = 210 (Oisín's runs).

    Show answer

    Short x = 5.5 km, medium y = 10.5 km, long z = 21.5 km.

  11. How is 0.75x + 0.9y + 0.45z = 15600 rewritten with integer coefficients?

    Show answer

    Divide every term by 0.15 (multiply by 20/3) to get 5x + 6y + 3z = 104000.

  12. Solve x + y + z = 18000, 5x + 6y + 3z = 104000, 6x + 5y + 3z = 91500 (concert tickets).

    Show answer

    Standing x = 2500, seated y = 15000, VIP z = 500.

Want to create your own cards? Create a free account. AI generation uses credits.