haya.Learning made clear
Solving by substitution sheet
3-mark answer frame

Solve the pair 2x + 3y = 13 and 3x − y = 3 by the substitution method.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. 2x + 3y = 13 ... (1) and 3x − y = 3 ... (2). To find: x and y.
  2. 2 · Write the method. In (2), y has coefficient −1, so write y in terms of x from (2).
  3. 3 · Express y. From (2): y = 3x − 3 ... (3)
  4. 4 · Substitute in (1). 2x + 3(3x − 3) = 13, so 2x + 9x − 9 = 13, 11x = 22 and x = 2.
  5. 5 · Substitute back. From (3): y = 3(2) − 3 = 3.
  6. 6 · Check and box the answer. (1): 2(2) + 3(3) = 13. (2): 3(2) − 3 = 3. Therefore x = 2, y = 3.

Scoring tip: Number the equations (1), (2), (3) and say which one you substitute into. It makes your method easy to follow and mark.