Solve by the elimination method: 5x + 3y = 21 and 2x − 5y = −4.

1. 1 · Write what is given and what is to be found. 5x + 3y = 21 ... (1) and 2x − 5y = −4 ... (2). To find: x and y.
2. 2 · Write the method. Make the coefficients of x equal: multiply (1) by 2 and (2) by 5.
3. 3 · Multiply.
   • 10x + 6y = 42 ... (3)
   • 10x − 25y = −20 ... (4)
4. 4 · Eliminate x. The x terms have the same sign, so subtract (4) from (3): 31y = 62, so y = 2.
5. 5 · Substitute back. In (1): 5x + 3(2) = 21, so 5x = 15 and x = 3.
6. 6 · Check and box the answer. (2): 2(3) − 5(2) = 6 − 10 = −4. Therefore x = 3, y = 2.

Scoring tip: When you subtract, put the whole equation in brackets. −(−25y) becomes +25y, and that sign is where most mistakes happen.