Evaluate: {\text{begin}array l 3x+2y=-4 }-x+y=(13)/(6)\text{end}array .

Expression: $\left\{\begin{array} { l } 3x+2y=-4 \\ -x+y=\frac{ 13 }{ 6 }\end{array} \right.$

Multiply both sides of the equation by $3$

$\left\{\begin{array} { l } 3x+2y=-4 \\ -3x+3y=\frac{ 13 }{ 2 }\end{array} \right.$

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

$\left( x, y\right)=\left( -\frac{ 5 }{ 3 }, \frac{ 1 }{ 2 }\right)$