Answer
$x=-\frac{1}{4} \\ y = \frac{1}{3}$
Work Step by Step
We are given the following two equations: $$ \frac{3}{x}-\frac{2}{y}=-18 \\ \frac{2}{x}+\frac{3}{y}=1$$ We solve for x in the first equation: $$x=-\frac{3y}{2(-1+9y)}$$ Plugging into the second equation: $$ \frac{2}{-\frac{3y}{2(-1+9y)}}+\frac{3}{y}=1 \\ -\frac{4(-1+9y)}{3y}+\frac{3}{y}=1 \\ -4(-1+9y)+9=3y\\ y=\frac{1}{3} $$ So, it follows: $$x=-\frac{3(\frac{1}{3})}{2(-1+9(\frac{1}{3}))}\\ x= -\frac{1}{4}$$
