Multiple choice

Solve the following pair of equations: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}=14$

  1. $x= 5;y= 6$
  2. $x= 3;y= 2$
  3. $x= 7;y= 4$
  4. $x= 0;y= 6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let u = 1/y. Equations: 4x + 6u = 15 and 6x - 8u = 14. Multiply first by 4 and second by 3: 16x + 24u = 60 and 18x - 24u = 42. Adding gives 34x = 102, so x = 3. Then 12 + 6/y = 15, so 6/y = 3, y = 2.

AI explanation

Multiply the first equation by 8 to get 32x + 48/y = 120, and multiply the second equation by 6 to get 36x - 48/y = 84. Adding these two equations eliminates the y term, resulting in 68x = 204, which gives x = 3. Substituting x = 3 into the first original equation yields 12 + 6/y = 15, so 6/y = 3 and y = 2. The solution is x = 3, y = 2.

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