In matrix form, the system can be expressed as
[tex]\begin{bmatrix}1&3&2\\1&-3&4\\2&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}26\\2\\8\end{bmatrix}[/tex]
Quick way to solve this: notice that adding the first two equations eliminates y, leaving you with
(x + 3y + 2z) + (x - 3y + 4z) = 26 + 2
2x + 6z = 28
x + 3z = 14
From the given answer choices, x has 2 possible values:
• If x = -10/7, we have
-10/7 + 3z = 14
3z = 108/7
z = 36/7 (so A is the correct answer)
• If x = -5/7, then
-6/7 + 3z = 14
3z = 104/7
z = 104/21 (which is not listed)
