Solve for: {\text{begin}array l 4x-3y=49 } 3x+5y=-14\text{end}array .

Expression: $\left\{\begin{array} { l } 4x-3y=49 \\ 3x+5y=-14\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } 4x=49+3y \\ 3x+5y=-14\end{array} \right.$

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

$\left( x, y\right)=\left( 7, -7\right)$