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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? (5 points)

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ANSWER

Step 2

EXPLANATION

The system of equations are:

Equation A:

[tex]y = 4 - 2z[/tex]

Equation B:

[tex]4y=2 - 4z[/tex]Step 1: Multiply equation A by -4.

Equation A:

[tex] - 4(y) = - 4(4 - 2z)[/tex]

Equation B:

[tex]4y=2 - 4z[/tex]

Step 2: Simplify equation A in step 1,

Equation A:

[tex] - 4y= - 16 + 8z[/tex]

This is where the student made the first error.

He didn't expand the second parenthesis correctly.

Answer:

The student made the first mistake in step 2.

Step-by-step explanation:

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