Solve for: {\text{begin}array l 2x+3y=6 } x+y=4\text{end}array .

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

Multiply both sides of the equation by $-2$

$\left\{\begin{array} { l } 2x+3y=6 \\ -2x-2y=-8\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$y=-2$

Substitute the given value of $y$ into the equation $x+y=4$

$x+\left( -2 \right)=4$

Solve the equation for $x$

$x=6$

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

$\left( x, y\right)=\left( 6, -2\right)$

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

$\left\{\begin{array} { l } 2 \times 6+3 \times \left( -2 \right)=6 \\ 6+\left( -2 \right)=4\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 6=6 \\ 4=4\end{array} \right.$

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

$\left( x, y\right)=\left( 6, -2\right)$