Multiple choice

Solve the following system of equations by elimination method. $\dfrac{15}{x}+\dfrac{2}{y}=17, \dfrac{1}{x}+\dfrac{1}{y}=\dfrac{36}{5}, x\neq 0, y\neq 0$

  1. $\left ( 5, \dfrac{1}{7} \right )$
  2. $\left ( 2, \dfrac{1}{7} \right )$
  3. $\left ( 5, \dfrac{2}{7} \right )$

  4. None of these
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A Correct answer
Explanation

Let u = 1/x and v = 1/y. Equations: 15u + 2v = 17 and u + v = 36/5. From second, u = 36/5 - v. Substitute: 15(36/5 - v) + 2v = 17 => 108 - 15v + 2v = 17 => 13v = 91 => v = 7. Then u = 36/5 - 7 = 1/5. So x = 5, y = 1/7.

AI explanation

By substituting u for 1/x and v for 1/y, the equations become 15u + 2v equals 17 and u + v equals 36/5. Multiplying the second equation by 2 gives 2u + 2v equals 72/5, and subtracting this from the first equation yields 13u equals 13/5, meaning u equals 1/5. Substituting u back gives 1/5 + v equals 36/5, so v equals 7. Because u is 1/x and v is 1/y, the values are x equals 5 and y equals 1/7.

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