Solve by elimination: x + y + z = 6, 2x − y + z = 3, x + 2y − z = 2.

1. 1 · Write what is given and what is to be found. Copy the three equations and number them (1), (2), (3). To find: x, y and z.
2. 2 · Write the method. State that you use the elimination method and that you remove z from two pairs.
3. 3 · Eliminate the same variable twice.
   • (1) + (3): 2x + 3y = 8 ... (4)
   • (2) + (3): 3x + y = 5 ... (5)
4. 4 · Solve the two-variable pair. 3 × (5) − (4): 7x = 7, so x = 1. Then (5) gives y = 2.
5. 5 · Substitute back. Put x = 1 and y = 2 in (1): z = 3.
6. 6 · Check and box the answer. In (2): 2 − 2 + 3 = 3. True. Box: x = 1, y = 2, z = 3.

Scoring tip: Number every new equation. Examiners give step marks for each correct elimination, even if the last arithmetic slips.