$\left\{\begin{array} { l } 2y=-7+3x \\ 5x+y=2\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } 2y=-7+3x \\ y=2-5x\end{array} \right.$
Divide both sides of the equation by $2$$\left\{\begin{array} { l } y=-\frac{ 7 }{ 2 }+\frac{ 3 }{ 2 }x \\ y=2-5x\end{array} \right.$
Since both expressions $-\frac{ 7 }{ 2 }+\frac{ 3 }{ 2 }x$ and $2-5x$ are equal to $y$, set them equal to each other forming an equation in $x$$-\frac{ 7 }{ 2 }+\frac{ 3 }{ 2 }x=2-5x$
Solve the equation for $x$$x=\frac{ 11 }{ 13 }$
Substitute the given value of $x$ into the equation $y=2-5x$$y=2-5 \times \frac{ 11 }{ 13 }$
Solve the equation for $y$$y=-\frac{ 29 }{ 13 }$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( \frac{ 11 }{ 13 }, -\frac{ 29 }{ 13 }\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } -3 \times \frac{ 11 }{ 13 }+2 \times \left( -\frac{ 29 }{ 13 } \right)=-7 \\ 5 \times \frac{ 11 }{ 13 }+\left( -\frac{ 29 }{ 13 } \right)=2\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } -7=-7 \\ 2=2\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( \frac{ 11 }{ 13 }, -\frac{ 29 }{ 13 }\right)$