$\left\{\begin{array} { l } x=2-\frac{ 2 }{ 3 }y \\ 5x+4y=8\end{array} \right.$
Substitute the given value of $x$ into the equation $5x+4y=8$$5\left( 2-\frac{ 2 }{ 3 }y \right)+4y=8$
Solve the equation for $y$$y=-3$
Substitute the given value of $y$ into the equation $x=2-\frac{ 2 }{ 3 }y$$x=2-\frac{ 2 }{ 3 } \times \left( -3 \right)$
Solve the equation for $x$$x=4$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 4, -3\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 3 \times 4+2 \times \left( -3 \right)=6 \\ 5 \times 4+4 \times \left( -3 \right)=8\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 6=6 \\ 8=8\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 4, -3\right)$