Multiple choice

Solve the following equations: $y(y^{2} - 3xy -x^{2}) + 24 = 0, x (y^{2} - 4xy + 2x^{2}) + 8 = 0$.

  1. $(2,4)$
  2. $(2,6)$
  3. $(3,4)$
  4. $(4,7)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Substitute the options into the equations. For (2,6): y=6, x=2. First eq: 6(36 - 3(2)(6) - 4) + 24 = 6(36 - 36 - 4) + 24 = 6(-4) + 24 = 0. Second eq: 2(36 - 4(2)(6) + 2(4)) + 8 = 2(36 - 48 + 8) + 8 = 2(-4) + 8 = 0. Both equations are satisfied.

AI explanation

We can check the given options directly in the provided equations. Substituting x = 2 and y = 6 into the first equation gives 6 times (36 minus 36 minus 4) plus 24, which equals 0. Substituting these same values into the second equation gives 2 times (36 minus 48 plus 8) plus 8, which also equals 0. The values x = 2 and y = 6 satisfy both equations.

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