$4x-3\left( -2x+3 \right)=1$
Solve the equation for $x$$x=1$
Substitute the given value of $x$ into the equation $y=-2x+3$$y=-2 \times 1+3$
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$\left\{\begin{array} { l } 1=-2 \times 1+3 \\ 4 \times 1-3 \times 1=1\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 1=1 \\ 1=1\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 1, 1\right)$