Multiple choice

Solve the following pair of linear equation: $\dfrac{5}{2x} + \dfrac{2}{3y} = 7, \, \dfrac{3}{x} + \dfrac{2}{y} = 12, \, x \neq 0 , \, y \neq 0$

  1. $x=\dfrac {1}{2},y=\dfrac {1}{4}$
  2. $x=\dfrac {1}{4},y=\dfrac {1}{3}$
  3. $x=\dfrac {1}{2},y=\dfrac {1}{3}$
  4. $x=\dfrac {1}{4},y=\dfrac {1}{6}$
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C Correct answer
Explanation

Let u=1/x, v=1/y. 5/2u + 2/3v = 7 => 15u + 4v = 42. 3u + 2v = 12 => 6u + 4v = 24. Subtracting: 9u = 18, u = 2, so x = 1/2. 6(2) + 4v = 24 => 4v = 12, v = 3, so y = 1/3.

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