Solve for: {\text{begin}array l x+y=-1 } x-y=9\text{end}array .

Expression: $\left\{\begin{array} { l } x+y=-1 \\ x-y=9\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$2x=8$

Divide both sides of the equation by $2$

$x=4$

Substitute the given value of $x$ into the equation $x+y=-1$

$4+y=-1$

Solve the equation for $y$

$y=-5$

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

$\left( x, y\right)=\left( 4, -5\right)$

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

$\left\{\begin{array} { l } 4+\left( -5 \right)=-1 \\ 4-\left( -5 \right)=9\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } -1=-1 \\ 9=9\end{array} \right.$

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

$\left( x, y\right)=\left( 4, -5\right)$