Make one letter disappear

Two equations, two unknowns. If the y terms match, adding or subtracting the equations removes y.

  1. 3x + 2y = 16
  2. 5x − 2y = 0
  3. add: 8x = 16, so x = 2
  4. substitute: 3 × 2 + 2y = 16, so y = 5
  5. check in the second: 5 × 2 − 2 × 5 = 0

Same signs: subtract. Opposite signs: add.

When the numbers do not match

Multiply one equation (or both) so that one letter has the same number in front.

  1. 2x + 3y = 13
  2. 5x + 2y = 16
  3. first × 2: 4x + 6y = 26
  4. second × 3: 15x + 6y = 48
  5. subtract: 11x = 22, so x = 2, then y = 3

Check with the solver

Choose Simultaneous, enter 2x + 3y = 13 and 5x + 2y = 16, and compare its steps with yours. Then change one number and predict how the answer moves.

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