$\left\{\begin{array} { l } 3x-8y=-6 \\ -10x+8y=20\end{array} \right.$
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$\left( x, y\right)=\left( -2, 0\right)$