Calculate: {\text{begin}array l x+2y=13 } 3x-5y=6\text{end}array .

Expression: $\left\{\begin{array} { l } x+2y=13 \\ 3x-5y=6\end{array} \right.$

Multiply both sides of the equation by $-3$

$\left\{\begin{array} { l } -3x-6y=-39 \\ 3x-5y=6\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$-11y=-33$

Divide both sides of the equation by $-11$

$y=3$

Substitute the given value of $y$ into the equation $3x-5y=6$

$3x-5 \times 3=6$

Solve the equation for $x$

$x=7$

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

$\left( x, y\right)=\left( 7, 3\right)$

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

$\left\{\begin{array} { l } 7+2 \times 3=13 \\ 3 \times 7-5 \times 3=6\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 13=13 \\ 6=6\end{array} \right.$

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

$\left( x, y\right)=\left( 7, 3\right)$