Maths · Rung 20 of 30

Systems of equations

Two equations with two unknowns: solve one for a variable and substitute into the other, or add the equations so one unknown disappears. Always check the solution in both.

Where this sits

This is where the ladder starts: nothing is needed before it.

Exercises from this rung

Generated by the app, from easiest to hardest

  1. 2x + 2y = 8 2x − 3y = −2 x = ?

    • 4
    • 2
    • 3
    • 1

    Why The solution is x = 2, y = 2: 2 × 2 + 2 × 2 = 8 and 2 × 2 − 3 × 2 = -2.

    easier

  2. x + 2y = 1 −x − 3y = 2 y = ?

    • -3
    • 7
    • 3
    • 0

    Why The solution is x = 7, y = -3: 1 × 7 + 2 × -3 = 1 and -1 × 7 − 3 × -3 = 2.

    in between

  3. 3x + 2y = −9 −x + 2y = 3 x = ?

    • 0
    • 3
    • -3
    • 1

    Why The solution is x = -3, y = 0: 3 × -3 + 2 × 0 = -9 and -1 × -3 + 2 × 0 = 3.

    harder