Evaluate: {\text{begin}array l 3x-8y=-6 }-5x+4y=10\text{end}array .

Expression: $\left\{\begin{array} { l } 3x-8y=-6 \\ -5x+4y=10\end{array} \right.$

Multiply both sides of the equation by $2$

$\left\{\begin{array} { l } 3x-8y=-6 \\ -10x+8y=20\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$-7x=14$

Divide both sides of the equation by $-7$

$x=-2$

Substitute the given value of $x$ into the equation $3x-8y=-6$

$3 \times \left( -2 \right)-8y=-6$

Solve the equation for $y$

$y=0$

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

$\left( x, y\right)=\left( -2, 0\right)$

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

$\left\{\begin{array} { l } 3 \times \left( -2 \right)-8 \times 0=-6 \\ -5 \times \left( -2 \right)+4 \times 0=10\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } -6=-6 \\ 10=10\end{array} \right.$

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

$\left( x, y\right)=\left( -2, 0\right)$