Evaluate: {\text{begin}array l x-2y=11 } x+5y=-17\text{end}array .

Expression: $\left\{\begin{array} { l } x-2y=11 \\ x+5y=-17\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } x=11+2y \\ x+5y=-17\end{array} \right.$

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

$\left( x, y\right)=\left( 3, -4\right)$