$\left\{\begin{array} { l } 3x+2y=-4 \\ -3x+3y=\frac{ 13 }{ 2 }\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$5y=\frac{ 5 }{ 2 }$
Divide both sides of the equation by $5$$y=\frac{ 1 }{ 2 }$
Substitute the given value of $y$ into the equation $-x+y=\frac{ 13 }{ 6 }$$-x+\frac{ 1 }{ 2 }=\frac{ 13 }{ 6 }$
Solve the equation for $x$$x=-\frac{ 5 }{ 3 }$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -\frac{ 5 }{ 3 }, \frac{ 1 }{ 2 }\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 3 \times \left( -\frac{ 5 }{ 3 } \right)+2 \times \frac{ 1 }{ 2 }=-4 \\ -\left( -\frac{ 5 }{ 3 } \right)+\frac{ 1 }{ 2 }=\frac{ 13 }{ 6 }\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } -4=-4 \\ \frac{ 13 }{ 6 }=\frac{ 13 }{ 6 }\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -\frac{ 5 }{ 3 }, \frac{ 1 }{ 2 }\right)$