Giải các hệ phương trình sau bằng phương pháp đặt ẩn phụ

$\text{ a)}\left\{\begin{array}{ll}\frac{15}{x}-\frac{7}{y}=9& \\ \frac{4}{x}+\frac{9}{y}=35.& \end{array}\right.$                                 

b) \(\left\{ {\begin{array}{*{20}{l}}{\frac{7}{{x - y + 2}} - \frac{5}{{x + y - 1}} = 4,5}\\{\frac{3}{{x - y + 2}} + \frac{2}{{x + y - 1}} = 4}\end{array}} \right.\)

a) Đặt \(u = \frac{1}{x},v = \frac{1}{y}(x \ne 0,y \ne 0)\). Ta được

\(\left\{ {\begin{array}{*{20}{l}}{15u - 7v = 9}\\{4u + 9v = 35}\end{array}} \right.\)\( \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{60u - 28v = 36}\\{60u + 135v = 525}\end{array}} \right.\)\( \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{163v = 489}\\{60u - 28v = 36}\end{array}} \right.\)\( \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{v = 3}\\{u = 2}\end{array}} \right.\)

Do đó \(x = \frac{1}{2},y = \frac{1}{3}\).

b) Đặt \(u = \frac{1}{{x - y + 2}},v = \frac{1}{{x + y - 1}},(x - y + 2 \ne 0,x + y - 1 \ne 0)\). Ta được

\(\left\{ {\begin{array}{*{20}{l}}{7u - 5v = 4,5}\\{3u + 2v = 4}\end{array}} \right.\)\( \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{14u - 10v = 9}\\{15u + 10v = 20}\end{array}} \right.\)\( \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{29u = 29}\\{7u - 5v = 4,5}\end{array}} \right.\)\( \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{u = 1}\\{v = \frac{1}{2}}\end{array}} \right.\)

Do đó \(\left\{ {\begin{array}{*{20}{l}}{x - y + 2 = 1}\\{x + y - 1 = \frac{1}{2}}\end{array}} \right.\)\( \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{x = \frac{1}{4}}\\{y = \frac{5}{4}}\end{array}} \right.\)