Calculate: {\text{begin}array l 4x+3y=35 } y=-2x-4\text{end}array .

Expression: $\left\{\begin{array} { l } 4x+3y=35 \\ y=-2x-4\end{array} \right.$

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

$\left\{\begin{array} { l } 3y=35-4x \\ y=-2x-4\end{array} \right.$

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

$\left( x, y\right)=\left( -\frac{ 47 }{ 2 }, 43\right)$