solve the equation

i ) xy / x + y = 6/5 & xy / y - x =6

ii) 99x+101y=499 & 101x+99y=501

Question

solve the equation
i ) xy / x + y = 6/5 & xy / y - x =6
ii) 99x+101y=499 & 101x+99y=501

Shridhar Kaushik · Accepted Answer

(1) We have, $\frac{x y}{x + y} = \frac{6}{5} and \frac{x y}{y - x} = 6 \Rightarrow \frac{x + y}{x y} = \frac{5}{6} and \frac{y - x}{x y} = \frac{1}{6} \Rightarrow \frac{x}{x y} + \frac{y}{x y} = \frac{5}{6} and \frac{y}{x y} - \frac{x}{x y} = \frac{1}{6} \Rightarrow \frac{1}{y} + \frac{1}{x} = \frac{5}{6} and \frac{1}{x} - \frac{1}{y} = \frac{1}{6}$ Taking $\frac{1}{x} = p and \frac{1}{y} = q$ , we get

$\Rightarrow p = \frac{1}{2}$ And so from (1), $q + \frac{1}{2} = \frac{5}{6}$ $\Rightarrow q = \frac{5}{6} - \frac{1}{2} = \frac{1}{3} Thus, x = \frac{1}{p} = 2 and y = \frac{1}{q} = 3$ (2) We have, 99x + 101y = 400 (1) 101x + 99y = 501 (2) Multiplying (1) by 101 and (2) by 99 and subtracting (2) from (1), we get

(10201 â€“ 9801)y = 50399 â€“ 49599 â‡’ 400y = 800 â‡’ y = 2 âˆ´ From (1), 99x + 202 = 499 â‡’ 99x = 297 â‡’ x = 3 Hence, x = 3 y = 2

solve the equation i ) xy / x + y = 6/5 & xy / y - x =6 ii) 99x+101y=499 & 101x+99y=501

solve the equation

i ) xy / x + y = 6/5 & xy / y - x =6

ii) 99x+101y=499 & 101x+99y=501