Calculate: {\text{begin}array l 5x+3y=-12 } 4x+3y=-9\text{end}array .

Expression: $\left\{\begin{array} { l } 5x+3y=-12 \\ 4x+3y=-9\end{array} \right.$

Solve the equation for $3y$

$\left\{\begin{array} { l } 5x+3y=-12 \\ 3y=-9-4x\end{array} \right.$

Substitute the given value of $3y$ into the equation $5x+3y=-12$

$5x-9-4x=-12$

Solve the equation for $x$

$x=-3$

Substitute the given value of $x$ into the equation $3y=-9-4x$

$3y=-9-4 \times \left( -3 \right)$

Solve the equation for $y$

$y=1$

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

$\left( x, y\right)=\left( -3, 1\right)$

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

$\left\{\begin{array} { l } 5 \times \left( -3 \right)+3 \times 1=-12 \\ 4 \times \left( -3 \right)+3 \times 1=-9\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } -12=-12 \\ -9=-9\end{array} \right.$

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

$\left( x, y\right)=\left( -3, 1\right)$