Question

(08.05)

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

Equation 1: m = 6 + n
Equation 2: 2m = 8 + 8n

Step 1: 
−2(m) = 
−2(6 + n)
 
2m = 
8 + 8n
 
Step 2: 
−2m = 
−12 − 2n
 
2m = 
8 + 8n
 
Step 3: 
−12 − 2n = 
8 + 8n
 
Step 4: 
−20 = 
10n
 
Step 5: 
n = 
−2


In which step did the student first make an error?

Step 2
Step 3
Step 4
Step 5

Answer 1

the mistake is in step 3:

I: −2m =−12 − 2n
II: 2m = 8 + 8n

the student set both right sides of the equations equal (−12 − 2n = 8 + 8n), but the left sides aren't equal: first equation has -2m, second has +2m so the signs of one of the equations must be inverted first