$\left\{\begin{array} { l } x=11+2y \\ x+5y=-17\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } x=11+2y \\ x=-17-5y\end{array} \right.$
Since both expressions $11+2y$ and $-17-5y$ are equal to $x$, set them equal to each other forming an equation in $y$$11+2y=-17-5y$
Solve the equation for $y$$y=-4$
Substitute the given value of $y$ into the equation $x=-17-5y$$x=-17-5 \times \left( -4 \right)$
Solve the equation for $x$$x=3$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 3, -4\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 3-2 \times \left( -4 \right)=11 \\ 3+5 \times \left( -4 \right)=-17\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 11=11 \\ -17=-17\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 3, -4\right)$