#### Answer

$(6,6)$

#### Work Step by Step

To eliminate y, multiply both equations with numbers so the coefficient of y is $\pm 6:$
$\left\{\begin{array}{llll}
3x & -2y & =6 & /\times 3\\
2x & -3y & =-6 & /\times(-2)
\end{array}\right.$
$\left\{\begin{array}{llll}
9x & -6y & =18 & \\
-4x & +6y & =12 &
\end{array}\right.$
... add and solve ...
$5x=30\qquad/\div 5$
$x=6$
Back substitute into one of the initial equations:
$3x-2y=6$
$3(6)-2y=6\qquad /-18$
$-2y=-12\qquad /\div(-2)$
$y=6$
Solutions are ordered pairs (x,y):
$(6,6)$
Check graphically by graphing both lines in the same window and determining the intersection (see image).