$\left\{\begin{array} { l } y=17+9x \\ -7x-10y=24\end{array} \right.$
Move the variable to the right-hand side and change its sign$\left\{\begin{array} { l } y=17+9x \\ -10y=24+7x\end{array} \right.$
Divide both sides of the equation by $-10$$\left\{\begin{array} { l } y=17+9x \\ y=-\frac{ 12 }{ 5 }-\frac{ 7 }{ 10 }x\end{array} \right.$
Since both expressions $17+9x$ and $-\frac{ 12 }{ 5 }-\frac{ 7 }{ 10 }x$ are equal to $y$, set them equal to each other forming an equation in $x$$17+9x=-\frac{ 12 }{ 5 }-\frac{ 7 }{ 10 }x$
Solve the equation for $x$$x=-2$
Substitute the given value of $x$ into the equation $y=-\frac{ 12 }{ 5 }-\frac{ 7 }{ 10 }x$$y=-\frac{ 12 }{ 5 }-\frac{ 7 }{ 10 } \times \left( -2 \right)$
Solve the equation for $y$$y=-1$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( -2, -1\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } -9 \times \left( -2 \right)+\left( -1 \right)=17 \\ -7 \times \left( -2 \right)-10 \times \left( -1 \right)=24\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 17=17 \\ 24=24\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( -2, -1\right)$