# Calculate: {\text{begin}array l 2x-3y=9 }-5x-3y=30\text{end}array .

## Expression: $\left\{\begin{array} { l } 2x-3y=9 \\ -5x-3y=30\end{array} \right.$

Multiply both sides of the equation by $-1$

$\left\{\begin{array} { l } 2x-3y=9 \\ 5x+3y=-30\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$7x=-21$

Divide both sides of the equation by $7$

$x=-3$

Substitute the given value of $x$ into the equation $2x-3y=9$

$2 \times \left( -3 \right)-3y=9$

Solve the equation for $y$

$y=-5$

The possible solution of the system is the ordered pair $\left( x, y\right)$

$\left( x, y\right)=\left( -3, -5\right)$

Check if the given ordered pair is the solution of the system of equations

$\left\{\begin{array} { l } 2 \times \left( -3 \right)-3 \times \left( -5 \right)=9 \\ -5 \times \left( -3 \right)-3 \times \left( -5 \right)=30\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 9=9 \\ 30=30\end{array} \right.$

Since all of the equalities are true, the ordered pair is the solution of the system

$\left( x, y\right)=\left( -3, -5\right)$

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