<s>[INST] Find $x$ and $y$ by Cramer from $\left\{\begin{aligned} \frac{2x+2}{2y-3}&=\frac{x-2}{y+3}\\ \frac{x+2}{3y-2}&=\frac{x-1}{3y+8} \end{aligned}\right.$ 
Find $x$ and $y$ with Cramer rule from these equations
  $$\left\{
\begin{aligned} 
\frac{2x+2}{2y-3}&=\frac{x-2}{y+3} \\
\frac{x+2}{3y-2}&=\frac{x-1}{3y+8}
\end{aligned} 
\right.
$$

I'm getting stuck to make the $x$ and $y$ out for making system equation matrix. Any idea?
 [/INST] I will show you the first one:
$$\frac{2x+2}{2y-3}=\frac{x-2}{y+3} \implies\\
(2x+2)(y+3)=(x-2)(2y-3)\implies\\
2xy+6x+2y+6=2xy-3x-4y+6$$
Can you see how you can cancel and combine the terms now?
</s>