# Calculate: {\text{begin}array l-9x+y=17 }-7x-10y=24\text{end}array .

## Expression: $\left\{\begin{array} { l } -9x+y=17 \\ -7x-10y=24\end{array} \right.$

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

$\left\{\begin{array} { l } y=17+9x \\ -7x-10y=24\end{array} \right.$

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

$\left( x, y\right)=\left( -2, -1\right)$

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