$\left\{\begin{array} { l } 3y=35-4x \\ y=-2x-4\end{array} \right.$
Divide both sides of the equation by $3$$\left\{\begin{array} { l } y=\frac{ 35 }{ 3 }-\frac{ 4 }{ 3 }x \\ y=-2x-4\end{array} \right.$
Since both expressions $\frac{ 35 }{ 3 }-\frac{ 4 }{ 3 }x$ and $-2x-4$ are equal to $y$, set them equal to each other forming an equation in $x$$\frac{ 35 }{ 3 }-\frac{ 4 }{ 3 }x=-2x-4$
Solve the equation for $x$$x=-\frac{ 47 }{ 2 }$
Substitute the given value of $x$ into the equation $y=-2x-4$$y=-2 \times \left( -\frac{ 47 }{ 2 } \right)-4$
Solve the equation for $y$$y=43$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -\frac{ 47 }{ 2 }, 43\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 4 \times \left( -\frac{ 47 }{ 2 } \right)+3 \times 43=35 \\ 43=-2 \times \left( -\frac{ 47 }{ 2 } \right)-4\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 35=35 \\ 43=43\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -\frac{ 47 }{ 2 }, 43\right)$