Evaluate: {\text{begin}array l X-3Y=3 } 2X=3Y\text{end}array .

Expression: $\left\{\begin{array} { l } X-3Y=3 \\ 2X=3Y\end{array} \right.$

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

$\left\{\begin{array} { l } -3Y=3-X \\ 2X=3Y\end{array} \right.$

Swap the sides of the equation

$\left\{\begin{array} { l } -3Y=3-X \\ 3Y=2X\end{array} \right.$

Multiply both sides of the equation by $-1$

$\left\{\begin{array} { l } 3Y=-3+X \\ 3Y=2X\end{array} \right.$

Since both expressions $-3+X$ and $2X$ are equal to $3Y$, set them equal to each other forming an equation in $X$

$-3+X=2X$

Solve the equation for $X$

$X=-3$

Substitute the given value of $X$ into the equation $3Y=2X$

$3Y=2 \times \left( -3 \right)$

Solve the equation for $Y$

$Y=-2$

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

$\left( X, Y\right)=\left( -3, -2\right)$

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

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

Simplify the equalities

$\left\{\begin{array} { l } 3=3 \\ -6=-6\end{array} \right.$

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

$\left( X, Y\right)=\left( -3, -2\right)$