$\left\{\begin{array} { l } 2y=6-3x \\ 5x+4y=8\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } 2y=6-3x \\ 4y=8-5x\end{array} \right.$
Divide both sides of the equation by $2$$\left\{\begin{array} { l } 2y=6-3x \\ 2y=4-\frac{ 5 }{ 2 }x\end{array} \right.$
Since both expressions $6-3x$ and $4-\frac{ 5 }{ 2 }x$ are equal to $2y$, set them equal to each other forming an equation in $x$$6-3x=4-\frac{ 5 }{ 2 }x$
Solve the equation for $x$$x=4$
Substitute the given value of $x$ into the equation $2y=4-\frac{ 5 }{ 2 }x$$2y=4-\frac{ 5 }{ 2 } \times 4$
Solve the equation for $y$$y=-3$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\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$\left( x, y\right)=\left( 4, -3\right)$