Question

Solve the following simultaneous equation.

\[\frac{148}{x} + \frac{231}{y} = \frac{527}{xy} ; \frac{231}{x} + \frac{148}{y} = \frac{610}{xy}\]

Answer 1

\[\frac{148}{x} + \frac{231}{y} = \frac{527}{xy} ; \frac{231}{x} + \frac{148}{y} = \frac{610}{xy}\]

Multiply by xy

148y + 231x = 527     ...(1)

231y + 148x = 610     ...(2)

Adding equation (1) and (2)

379y + 379x = 1137

x + y = 3       ...(3)

(2) - (1)

83y - 83x = 83

⇒ y - x = 1      ...(4)

Adding equation (3) + (4)

2y = 4

⇒ y = 2

Putting the value of y in (4)

2 - x = 1

⇒ x = 1

(x, y) = (1, 2)