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Solve the following pairs of equations by reducing them to a pair of linear equations:
(i) \( \frac{1}{2 x}+\frac{1}{3 y}=2 \)
(ii) \( \frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2 \)
IV
\( -\quad \frac{1}{3 x}+\frac{1}{2 y}=\frac{13}{6} \)
\[
\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1
\]
(iii) \( \frac{4}{x}+3 y=14 \)
(iv) \( \frac{5}{x-1}+\frac{1}{y-2}=2 \)
\( -\quad \frac{3}{x}-4 y=23 \) \( \frac{6}{x-1}-\frac{3}{y-2}=1 \)
- (v) \( \frac{7 x-2 y}{x y}=5 \)
(vi) \( 6 x+3 y=6 x y \)
\[
\frac{8 x+7 y}{x y}=15
\]
\[
2 x+4 y=5 x y
\]
(vii) \( \frac{10}{x+y}+\frac{2}{x-y}=4 \)
(viii) \( \frac{1}{3 x+y}+\frac{1}{3 x-y}=\frac{3}{4} \) \( \frac{15}{x+y}-\frac{5}{x-y}=-2 \) \( \frac{1}{2(3 x+y)}-\frac{1}{2(3 x-y)}=\frac{-1}{8} \)
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