Solve for $\mathrm{x}$ and $\mathrm{y}$:

$\frac{1}{2\mathrm{x}}+\frac{1}{3\mathrm{y}}=2$

$\frac{1}{3\mathrm{x}}+\frac{1}{2\mathrm{y}}=\frac{13}{6}$

Solve for $x$ and $y$:

$\frac{5}{x+y}-\frac{2}{x-y}=-1, \frac{15}{x+y}+\frac{7}{x-y}=10$

Solve for $\mathrm{x}$ and $\mathrm{y}$ and find the sum of $x$ and $y$.

$\frac{3}{\mathrm{x}+\mathrm{y}}+\frac{2}{\mathrm{x}-\mathrm{y}}=2,\frac{9}{\mathrm{x}+\mathrm{y}}-\frac{4}{\mathrm{x}-\mathrm{y}}=1$, where $\mathrm{x}+\mathrm{y}\ne 0$ and $\mathrm{x}-\mathrm{y}\ne 0$

Solve for $x$ and $y$:

$\frac{44}{x+y}+\frac{30}{x-y}=10, \frac{55}{x+y}+\frac{40}{x-y}=13$

Solve for $x$ and $y$:

$\frac{10}{x+y}+\frac{2}{x-y}=4, \frac{15}{x+y}-\frac{9}{x-y}=-2$