​ Solve the following systems of equations: xy/(x+y) = 6/5 xy/(y-x) = 6 where, x + y ≠ 0 and x - y ≠ 0 ​

Question

Solve the following systems of equations:

\(\frac{xy}{x+y}\) = \(\frac{6}{5}\)

\(\frac{xy}{y-x}\) = 6

where, x + y ≠ 0 and x - y ≠ 0

Answer 1

 \(\frac{xy}{x+y}\) = \(\frac{6}{5}\)

\(\frac{xy}{y-x}\) = 6

Dividing the two equations

⇒ (y – x )/(x + y) = 1/5

⇒ 5y – 5x = x + y

⇒ y = 3x/2

Thus,

x x \(\cfrac{\frac{3x}{2}}{x+\frac{3x}{2}}\) = \(\frac{6}{5}\)

⇒ 3x/5 = 6/5

⇒ x = 2

Thus,

y = 3