# Solve for: {\text{begin}array l-5x-4y-z=8 }-4x-4y+2z=-6 x-5y-5z=36\text{end}array .

## Expression: $\left\{\begin{array} { l } -5x-4y-z=8 \\ -4x-4y+2z=-6 \\ x-5y-5z=36\end{array} \right.$

Write the coefficients of each equation as rows in the matrix

$\left\{\begin{array} { l } -5x-4y-z=8 \\ -4x-4y+2z=-6 \\ x-5y-5z=36\end{array} \right.$

Convert the augmented matrix into a system of linear equations

$\left\{\begin{array} { l } z=-5 \\ y=-2 \\ x=1\end{array} \right.$

The possible solution of the system is the ordered triple $\left( x, y, z\right)$

$\left( x, y, z\right)=\left( 1, -2, -5\right)$

Check if the given ordered triple is a solution of the system of equations

$\left\{\begin{array} { l } -5 \times 1-4 \times \left( -2 \right)-\left( -5 \right)=8 \\ -4 \times 1-4 \times \left( -2 \right)+2 \times \left( -5 \right)=-6 \\ 1-5 \times \left( -2 \right)-5 \times \left( -5 \right)=36\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 8=8 \\ -6=-6 \\ 36=36\end{array} \right.$

Since all of the equalities are true, the ordered triple is the solution of the system

$\left( x, y, z\right)=\left( 1, -2, -5\right)$

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