Solve the system, if possible.

Name: Solve the system, if possible.
Brand: Quizplus
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Question

Quizplus · Accepted Answer

By substitution, the second equation becomes $2x-y=24.$ Adding this with the first equation gives $3x+z=16.$ Solving for $z$ in the third equation and substituting for $z$ in the fourth equation gives $x-y=6.$ Solving the system $$\begin{cases} 3x+z=16 \ x-y=6 \end{cases}$$ gives $x=4$ and $y=-2,$ and solving for $z$ in the third equation gives $z=-24-4+2=-26.$ Thus $(x,y,z)=(4,-2,-26),$ which matches (C).

Solve the System, If Possible