Multiple choice

Solve each pair of equation by using the substitution method. $x+\dfrac{6}{y}=6$ $3x-\dfrac{8}{y}=5$

  1. $x=3$ and $y=-2$
  2. $x=30$ and $y=2$
  3. $x=3$ and $y=2$

  4. None of these
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C Correct answer
Explanation

Given x + 6/y = 6 and 3x - 8/y = 5. Let u = 1/y. x + 6u = 6 => x = 6 - 6u. Substitute into second: 3(6 - 6u) - 8u = 5 => 18 - 18u - 8u = 5 => 13 = 26u => u = 1/2. So y = 2. Then x = 6 - 6(1/2) = 6 - 3 = 3.

AI explanation

Using the elimination method, multiply the first equation by 3 to get 3x + 18/y = 18. Subtracting the second equation, 3x - 8/y = 5, from this result gives 26/y = 13. Solving for y yields y = 2. Substituting y = 2 into the first equation gives x + 3 = 6, so x = 3.

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