$\left\{\begin{array} { l } 4x=49+3y \\ 3x+5y=-14\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } 4x=49+3y \\ 3x=-14-5y\end{array} \right.$
Divide both sides of the equation by $4$$\left\{\begin{array} { l } x=\frac{ 49 }{ 4 }+\frac{ 3 }{ 4 }y \\ 3x=-14-5y\end{array} \right.$
Divide both sides of the equation by $3$$\left\{\begin{array} { l } x=\frac{ 49 }{ 4 }+\frac{ 3 }{ 4 }y \\ x=-\frac{ 14 }{ 3 }-\frac{ 5 }{ 3 }y\end{array} \right.$
Since both expressions $\frac{ 49 }{ 4 }+\frac{ 3 }{ 4 }y$ and $-\frac{ 14 }{ 3 }-\frac{ 5 }{ 3 }y$ are equal to $x$, set them equal to each other forming an equation in $y$$\frac{ 49 }{ 4 }+\frac{ 3 }{ 4 }y=-\frac{ 14 }{ 3 }-\frac{ 5 }{ 3 }y$
Solve the equation for $y$$y=-7$
Substitute the given value of $y$ into the equation $x=-\frac{ 14 }{ 3 }-\frac{ 5 }{ 3 }y$$x=-\frac{ 14 }{ 3 }-\frac{ 5 }{ 3 } \times \left( -7 \right)$
Solve the equation for $x$$x=7$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 7, -7\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 4 \times 7-3 \times \left( -7 \right)=49 \\ 3 \times 7+5 \times \left( -7 \right)=-14\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 49=49 \\ -14=-14\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 7, -7\right)$