$\left\{\begin{array} { l } -x+4y=4 \\ y=-x-9\end{array} \right.$
Simplify the expression$\left\{\begin{array} { l } -x+4y=4 \\ x+y=-9\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$5y=-5$
Divide both sides of the equation by $5$$y=-1$
Substitute the given value of $y$ into the equation $-x+4y=4$$-x+4 \times \left( -1 \right)=4$
Solve the equation for $x$$x=-8$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -8, -1\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } -1=\frac{ 1 }{ 4 } \times \left( -8 \right)+1 \\ -1=-\left( -8 \right)-9\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } -1=-1 \\ -1=-1\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -8, -1\right)$