$\left\{\begin{array} { l } -15x+12y=-27 \\ 2x-3y=5\end{array} \right.$
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$\left( x, y\right)=\left( 1, -1\right)$