Calculate: {\text{begin}array l-x+3y=-15 } 3x+3y=21\text{end}array .

Expression: $\left\{\begin{array} { l } -x+3y=-15 \\ 3x+3y=21\end{array} \right.$

Solve the equation for $3y$

$\left\{\begin{array} { l } 3y=-15+x \\ 3x+3y=21\end{array} \right.$

Substitute the given value of $3y$ into the equation $3x+3y=21$

$3x-15+x=21$

Solve the equation for $x$

$x=9$

Substitute the given value of $x$ into the equation $3x+3y=21$

$3 \times 9+3y=21$

Solve the equation for $y$

$y=-2$

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

$\left( x, y\right)=\left( 9, -2\right)$

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

$\left\{\begin{array} { l } -9+3 \times \left( -2 \right)=-15 \\ 3 \times 9+3 \times \left( -2 \right)=21\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } -15=-15 \\ 21=21\end{array} \right.$

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

$\left( x, y\right)=\left( 9, -2\right)$