Solve for: {\text{begin}array l 3x+5y=7 } 2x+3y=5\text{end}array .

Expression: $\left\{\begin{array} { l } 3x+5y=7 \\ 2x+3y=5\end{array} \right.$

Multiply both sides of the equation by $2$

$\left\{\begin{array} { l } 6x+10y=14 \\ 2x+3y=5\end{array} \right.$

Multiply both sides of the equation by $-3$

$\left\{\begin{array} { l } 6x+10y=14 \\ -6x-9y=-15\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$y=-1$

Substitute the given value of $y$ into the equation $2x+3y=5$

$2x+3 \times \left( -1 \right)=5$

Solve the equation for $x$

$x=4$

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

$\left( x, y\right)=\left( 4, -1\right)$

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

$\left\{\begin{array} { l } 3 \times 4+5 \times \left( -1 \right)=7 \\ 2 \times 4+3 \times \left( -1 \right)=5\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 7=7 \\ 5=5\end{array} \right.$

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

$\left( x, y\right)=\left( 4, -1\right)$