Given
\(\frac{2}{x}\) +\(\frac{3}{y}\) = 13 and
\(\frac{5}{x}\) – \(\frac{4}{y}\)= -2
Take \(\frac{1}{x}
\)= a and \(\frac{1}{y}\)= b,
then the given equations reduce to
2a + 3b = 13 ……… (1)
5a – 4b = -2 ……… (2)
⇒ b = \(\frac{69}{23}\) = 3
Substituting b = 3 in equation (1) we get
2a + 3 (3) = 13
⇒ 2a = 13 – 9
⇒ a =\(\frac{4}{2}\) = 2
but a =\(\frac{1}{x}\) = 2 ⇒ x = \(\frac{1}{2}\)
b =\(\frac{1}{y}\) = 3 ⇒ y = \(\frac{1}{3}\)
∴ Solution (x, y) = \((\frac{1}{2},\frac{1}{3})\)
