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

The answer is step 3

Explanation:

It is because Ernesto didn't distribute correctly, he only distributed 3 to the y and not the 7.

Answer 2

The answer is Step 3: 3y + 7 _ 2y = 8.

Ernesto made a mistake in the step 3 because he did not multiply 3 and 7.
The correct order of steps is:

Step 1: x = y + 7
Step 2: 3(y + 7) - 2y = 8
Step 3: 3y + 3·7 - 2y = 8
Step 4: y + 21 = 8
Step 5: y = - 13