Evaluate: {\text{begin}array l 5x-4y=9 } 2x-3y=5\text{end}array .

Expression: $\left\{\begin{array} { l } 5x-4y=9 \\ 2x-3y=5\end{array} \right.$

Multiply both sides of the equation by $-3$

$\left\{\begin{array} { l } -15x+12y=-27 \\ 2x-3y=5\end{array} \right.$

Multiply both sides of the equation by $4$

$\left\{\begin{array} { l } -15x+12y=-27 \\ 8x-12y=20\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$-7x=-7$

Divide both sides of the equation by $-7$

$x=1$

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

$2 \times 1-3y=5$

Solve the equation for $y$

$y=-1$

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

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

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

$\left\{\begin{array} { l } 5 \times 1-4 \times \left( -1 \right)=9 \\ 2 \times 1-3 \times \left( -1 \right)=5\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 9=9 \\ 5=5\end{array} \right.$

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

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