\left \{ {{x+y=2} \atop {12x+18y=32}} \right.
\left \{ {{x=2-y} \atop {12(2-y)+18y=32}} \right.
\left \{ {{x=2-y} \atop {24-12y+18y=32}} \right.
\left \{ {{x=2-y} \atop {24+6y=32}} \right.
\left \{ {{x=2-y} \atop {6y=32-24}} \right.
\left \{ {{x=2-y} \atop {6y=8}} \right.
\left \{ {{x=2-y} \atop {y=1\frac{2}{6}=1\frac{1}{3}}} \right.
\left \{ {{x=2-1\frac{1}{3}} \atop {y=1\frac{2}{6}=1\frac{1}{3}}} \right.
\left \{ {{x=\frac{2}{3}} \atop {y=1\frac{1}{3}}} \right.