Question

The work of a student to solve a set of equations is shown below:Equation 1: m = 8 + 2n Equation 2: 4m = 4 + 4nStep 1: −4(m) = −4(8 + 2n)4m = 4 + 4nStep 2: −4m = −32 − 8n4m = 4 + 4nStep 3: −4m + 4m = −32 − 8n + 4nStep 4: 0 = −32 − 4nStep 5: n = − 8In which step did the student first make an error? (4 points)a. Step 1b. Step 2c. Step 3d. Step 4

Answer 1

Given:

m = 8 + 2n

4m = 4 + 4n

Let's follow the steps shown to find out the step with the error.

Step 1:

Multiply equation 1 by -4

-4(m) = -4(8 + 2n)

4m = 4 + 4n

Step 2:

-4m = -32 - 8n

4m = 4 + 4n

Step 3:

Use elimination method to simplify

-4m = -32 - 8n

4m = 4 + 4n

-4m + 4m = -32 + 4 -8n + 4n

This is where the student made the first error, because "4" was ommited.

This error led to subsequent errors in step 4 and 5

Step 4:

0 = -28 - 4n

Add 4n to both sides

0 + 4n = -28 - 4n + 4n

4n = -28

Step 5:

Divide both sides by 4

`\begin{gathered} (4n)/(4)=(-28)/(4) \\ \\ n\text{ = -7} \end{gathered}`

ANSWER:

The student first made an error in step 3.