Question

Solve: $\frac{4}{x}+\frac{5}{y}=7$ and $\frac{3}{x}+\frac{4}{y}=5$

Answer 1

$\frac{4}{x}+\frac{5}{y}=7$ _______(1)

$\frac{3}{x}+\frac{4}{y}=5$ ______ (2)

multiplying (2) by 4 & (1) by 3

$\frac{12}{x}+\frac{15}{y}=21$

$\frac{12}{x}+\frac{16}{y}=20$

- - -

________________

$-\frac{1}{y}=1$ $\therefore y=-1$

$\frac{4}{x}+\frac{5}{-1}=7$

$=\frac{4}{x}=7+5$

$=\frac{4}{x}=12\Rightarrow x=\frac{1}{3}$

Hence $x=\frac{1}{3},y=-1$