# Calculate: {\text{begin}array l (x)/(3)-(y)/(2)=-3 } (x)/(6)+(y)/(5)=3\text{end}array .

## Expression: $\left\{\begin{array} { l } \frac{ x }{ 3 }-\frac{ y }{ 2 }=-3 \\ \frac{ x }{ 6 }+\frac{ y }{ 5 }=3\end{array} \right.$

Multiply both sides of the equation by $6$

$\left\{\begin{array} { l } 2x-3y=-18 \\ \frac{ x }{ 6 }+\frac{ y }{ 5 }=3\end{array} \right.$

Multiply both sides of the equation by $30$

$\left\{\begin{array} { l } 2x-3y=-18 \\ 5x+6y=90\end{array} \right.$

Multiply both sides of the equation by $2$

$\left\{\begin{array} { l } 4x-6y=-36 \\ 5x+6y=90\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$9x=54$

Divide both sides of the equation by $9$

$x=6$

Substitute the given value of $x$ into the equation $2x-3y=-18$

$2 \times 6-3y=-18$

Solve the equation for $y$

$y=10$

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

$\left( x, y\right)=\left( 6, 10\right)$

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

$\left\{\begin{array} { l } \frac{ 6 }{ 3 }-\frac{ 10 }{ 2 }=-3 \\ \frac{ 6 }{ 6 }+\frac{ 10 }{ 5 }=3\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } -3=-3 \\ 3=3\end{array} \right.$

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

$\left( x, y\right)=\left( 6, 10\right)$

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