Answer
$(-1,5,0)$
Work Step by Step
Step 1. Based on the Cramer’s Rule, with the given equations, we can define the following determinants:
(use $x,y,z$ to represent $a,b,c$)
$\begin{array}( \\|D|= \\ \\ \end{array}
\begin{vmatrix}-2 &0&1\\1&2&-1\\3&5&2 \end{vmatrix},
\begin{array}( \\|D_x|= \\ \\ \end{array}
\begin{vmatrix}2 &0&1\\9&2&-1\\22&5&2 \end{vmatrix},
\begin{array}( \\|D_y|= \\ \\ \end{array}
\begin{vmatrix}-2 &2&1\\1&9&-1\\3&22&2 \end{vmatrix},
\begin{array}( \\|D_z|= \\ \\ \end{array}
\begin{vmatrix}-2 &0&2\\1&2&9\\3&5&22 \end{vmatrix}$
Step 2. Evaluate the above determinants:
$|D|=(-2)(4+5)-(0)+(1)(5-6)=-19$ (row1 expansion),
$|D_x|=(2)(4+5)-(0)+(1)(45-44)=19$ (row1 expansion),
$|D_y|=(-2)(18+22)-(2)(2+3)+(1)(22-27)=-95$ (row1 expansion),
$|D_z|=(-2)(44-45)-(0)+(2)(5-6)=0$ (row1 expansion)
Step 3. Find the solutions as:
$x=\frac{|D_x|}{|D|}=-1$,
$y=\frac{|D_y|}{|D|}=5$,
$z=\frac{|D_z|}{|D|}=0$
