$\left\{\begin{array} { l } 3y+5x+57-7x-3x+11y=-23 \\ 4y+9x-y-20=5x-11-8x\end{array} \right.$
Move the constant to the right-hand side and change its sign$\left\{\begin{array} { l } 3y+5x-7x-3x+11y=-23-57 \\ 4y+9x-y-20=5x-11-8x\end{array} \right.$
Move the variables to the left-hand side and change their signs$\left\{\begin{array} { l } 3y+5x-7x-3x+11y=-23-57 \\ 4y+9x-y-20-5x+8x=-11\end{array} \right.$
Move the constant to the right-hand side and change its sign$\left\{\begin{array} { l } 3y+5x-7x-3x+11y=-23-57 \\ 4y+9x-y-5x+8x=-11+20\end{array} \right.$
Collect like terms$\left\{\begin{array} { l } 14y+5x-7x-3x=-23-57 \\ 4y+9x-y-5x+8x=-11+20\end{array} \right.$
Collect like terms$\left\{\begin{array} { l } 14y-5x=-23-57 \\ 4y+9x-y-5x+8x=-11+20\end{array} \right.$
Calculate the difference$\left\{\begin{array} { l } 14y-5x=-80 \\ 4y+9x-y-5x+8x=-11+20\end{array} \right.$
Collect like terms$\left\{\begin{array} { l } 14y-5x=-80 \\ 3y+9x-5x+8x=-11+20\end{array} \right.$
Collect like terms$\left\{\begin{array} { l } 14y-5x=-80 \\ 3y+12x=-11+20\end{array} \right.$
Calculate the sum$\left\{\begin{array} { l } 14y-5x=-80 \\ 3y+12x=9\end{array} \right.$
Use the commutative property to reorder the terms$\left\{\begin{array} { l } -5x+14y=-80 \\ 3y+12x=9\end{array} \right.$
Use the commutative property to reorder the terms$\left\{\begin{array} { l } -5x+14y=-80 \\ 12x+3y=9\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } 14y=-80+5x \\ 12x+3y=9\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } 14y=-80+5x \\ 3y=9-12x\end{array} \right.$
Divide both sides of the equation by $14$$\left\{\begin{array} { l } y=-\frac{ 40 }{ 7 }+\frac{ 5 }{ 14 }x \\ 3y=9-12x\end{array} \right.$
Divide both sides of the equation by $3$$\left\{\begin{array} { l } y=-\frac{ 40 }{ 7 }+\frac{ 5 }{ 14 }x \\ y=3-4x\end{array} \right.$
Since both expressions $-\frac{ 40 }{ 7 }+\frac{ 5 }{ 14 }x$ and $3-4x$ are equal to $y$, set them equal to each other forming an equation in $x$$-\frac{ 40 }{ 7 }+\frac{ 5 }{ 14 }x=3-4x$
Solve the equation for $x$$x=2$
Substitute the given value of $x$ into the equation $y=3-4x$$y=3-4 \times 2$
Solve the equation for $y$$y=-5$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 2, -5\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 3 \times \left( -5 \right)+5 \times 2+57-7 \times 2=3 \times 2-11 \times \left( -5 \right)-23 \\ 4 \times \left( -5 \right)+9 \times 2-\left( -5 \right)-20=5 \times 2-11-8 \times 2\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 38=38 \\ -17=-17\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 2, -5\right)$