Replace the letter

  1. y = 2x − 3
  2. 3x + 2y = 15
  3. replace y: 3x + 2(2x − 3) = 15
  4. 7x − 6 = 15, so x = 3
  5. y = 2 × 3 − 3 = 3

Brackets matter: 2(2x − 3), not 2 × 2x − 3.

If neither equation has a letter on its own, rearrange the easier one first: x + 3y = 11 gives x = 11 − 3y.

Two expressions for y

y = 3x + 1 and y = x + 7 are both equal to y, so 3x + 1 = x + 7. That gives x = 3 and y = 10. This is also where the two lines cross.