Solve for: {\text{begin}array l x-y+z=-8 } 4x+2y-z=12-2x+4y-z=36\text{end}array .
Expression: $\left\{\begin{array} { l } x-y+z=-8 \\ 4x+2y-z=12 \\ -2x+4y-z=36\end{array} \right.$
Rewrite the system as two systems, each consisting of two equations
$\begin{array} { l }\left\{\begin{array} { l } x-y+z=-8 \\ 4x+2y-z=12\end{array} \right.,\\\left\{\begin{array} { l } x-y+z=-8 \\ -2x+4y-z=36\end{array} \right.\end{array}$
Solve the system of equations
$\begin{array} { l }5x+y=4,\\\left\{\begin{array} { l } x-y+z=-8 \\ -2x+4y-z=36\end{array} \right.\end{array}$
$\begin{array} { l }5x+y=4,\\-x+3y=28\end{array}$
Write as a system of equations
$\left\{\begin{array} { l } 5x+y=4 \\ -x+3y=28\end{array} \right.$
$\begin{array} { l }x=-1,\\y=9\end{array}$
Substitute the given values of $\begin{array} { l }x,& y\end{array}$ into the equation $x-y+z=-8$
$-1-9+z=-8$
Solve the equation for $z$
$z=2$
The possible solution of the system is the ordered triple $\left( x, y, z\right)$
$\left( x, y, z\right)=\left( -1, 9, 2\right)$
Check if the given ordered triple is a solution of the system of equations
$\left\{\begin{array} { l } -1-9+2=-8 \\ 4 \times \left( -1 \right)+2 \times 9-2=12 \\ -2 \times \left( -1 \right)+4 \times 9-2=36\end{array} \right.$
Simplify the equalities
$\left\{\begin{array} { l } -8=-8 \\ 12=12 \\ 36=36\end{array} \right.$
Since all of the equalities are true, the ordered triple is the solution of the system
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