Solve for $x$ and $y$.

$$\begin{gathered} \frac{5}{x+1}-\frac{2}{y-1}=\frac{1}{2} \\ \frac{10}{x+1}+\frac{2}{y-1}=\frac{5}{2}, x\ne -1,y\ne 1 \end{gathered}$$

Solve for $x$ and $y$ by using method of substitution.

$$\begin{gathered} \frac{6}{x+y}-\frac{7}{x-y}=3 \\ \frac{1}{2(x+y)}-\frac{1}{3(x-y)}=0, x+y\ne 0, x-y\ne 0 \end{gathered}$$

Solve for $x$ and $y$.

$$\begin{gathered} 27x+31y=85 \\ 31x+27y=89 \end{gathered}$$

Solve for $x$ and $y$.

$$\begin{gathered} 37x-39y=150 \\ 39x-37y=154 \end{gathered}$$

Solve for $x$ and $y$.

$$\begin{gathered} \frac{148}{x}+\frac{231}{y}=\frac{527}{xy} \\ \frac{231}{x}+\frac{148}{y}=\frac{610}{xy} \end{gathered}$$