Evaluate: {\text{begin}array l x+y=30 } 3x-2y=30\text{end}array .

Expression: $\left\{\begin{array} { l } x+y=30 \\ 3x-2y=30\end{array} \right.$

Multiply both sides of the equation by $-3$

$\left\{\begin{array} { l } -3x-3y=-90 \\ 3x-2y=30\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$-5y=-60$

Divide both sides of the equation by $-5$

$y=12$

Substitute the given value of $y$ into the equation $x+y=30$

$x+12=30$

Solve the equation for $x$

$x=18$

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

$\left( x, y\right)=\left( 18, 12\right)$

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

$\left\{\begin{array} { l } 18+12=30 \\ 3 \times 18-2 \times 12=30\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 30=30 \\ 30=30\end{array} \right.$

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

$\left( x, y\right)=\left( 18, 12\right)$