Elementary row operations

Question

Which of the following can be used to cancel the z term from equation 2 in the following system of equations?

x+y+z=1 (Eq.1)

x+y-2z=-2(Eq.2)

3×-2y+z=6(Eq.3)

A. (Eq.1)+(Eq.2)

B.-(Eq.1)+(Eq.2)

C.2(Eq.1)+(Eq.2)

D. -2(Eq.1)+(Eq.2)

Answer 1

Evaluating Answer A): If you add eq 1 and eq 2 together, you would have:

x+y+z=1

x+y-2z=-2

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2x + 2y - z = -1 (z term not canceled)

Evaluating Answer B): If you add minus eq 1 and eq 2 together, you would have:

-x-y-z=-1

x+y-2z=-2

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0x + 0y - 3z = -3 (z term not canceled)

Evaluating Answer C): If you add 2 times eq 1 and eq 2 together, you would have:

2x+2y+2z=2

x+y-2z=-2

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3x + 3y +0z = 0 (z term IS canceled so (c) is the answer)

Evaluating Answer D): If you add -2 times eq 1 and eq 2 together, you would have:

-2x-2y-2z=-2

x+y-2z=-2

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-x - y - 4z = -4 (z term not canceled)