# Evaluate: {\text{begin}array l 4x-5y=18 } 6x+10y=-78\text{end}array .

## Expression: $\left\{\begin{array} { l } 4x-5y=18 \\ 6x+10y=-78\end{array} \right.$

Write the coefficients of each equation as rows in the matrix

$\left\{\begin{array} { l } 4x-5y=18 \\ 6x+10y=-78\end{array} \right.$

Convert the augmented matrix into a system of linear equations

$\left\{\begin{array} { l } y=-6 \\ x=-3\end{array} \right.$

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

$\left( x, y\right)=\left( -3, -6\right)$

Check if the given ordered pair is the solution of the system of equations

$\left\{\begin{array} { l } 4 \times \left( -3 \right)-5 \times \left( -6 \right)=18 \\ 6 \times \left( -3 \right)+10 \times \left( -6 \right)=-78\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 18=18 \\ -78=-78\end{array} \right.$

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

$\left( x, y\right)=\left( -3, -6\right)$

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