Evaluate: {\text{begin}array l y=-2x+3 } 4x-3y=1\text{end}array .

Expression: $\left\{\begin{array} { l } y=-2x+3 \\ 4x-3y=1\end{array} \right.$

Substitute the given value of $y$ into the equation $4x-3y=1$

$4x-3\left( -2x+3 \right)=1$

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

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