Question

The work of a student to solve a set of equations is shown:

Equation A: y = 4 − 2z
Equation B: 4y = 2 − 4z


Step 1: −4(y) = −4(4 − 2z) [Equation A is multiplied by −4.]
4y = 2 − 4z [Equation B]
Step 2: −4y = 4 − 2z [Equation A in Step 1 is simplified.]
4y = 2 − 4z [Equation B]
Step 3: 0 = 6 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 6
Step 5: z = 1


In which step did the student first make an error?
Step 1
Step 3
Step 4
Step 2

Answer 1

The student first made an error in step 2 when she simplified... She should have used the distributive property to distribute the -4 through the parentheses. It should look like this...

-4 (y) = -4 (4 - 2z)
-4y = -16 + 8z