Question

Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.

x – y = 7

3x – 2y = 8

Step 1: x = y + 7
Step 2: 3(y + 7) – 2y = 8
Step 3: 3y + 7 – 2y = 8
Step 4: y + 7 = 8
Step 5: y = 1

In which step did Ernesto make the first error?

Step 1
Step 2
Step 3
Step 4

Answer 1

Step 3.

He expanded 3(y + 7) incorrectly. It should be 3y + 21, not 3y + 7. (Correct work: 3y + 21 − 2y = 8 → y + 21 = 8 → y = −13, then x = −6.)