Multiple choice

Solve the following equations: $xy + ab = 2ax, x^{2}y^{2} + a^{2}b^{2} = 2b^{2}y^{2}$.

  1. $(b,a)$
  2. $(a,b)$
  3. $(-2a,b)$
  4. $(a,-b)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given xy + ab = 2ax and x^2y^2 + a^2b^2 = 2b^2y^2. Substituting y = (2ax - ab)/x into the second equation allows solving for x and y. Testing (b,a): b*a + ab = 2ab (True). b^2*a^2 + a^2*b^2 = 2a^2b^2. 2b^2*a^2 = 2b^2*a^2 (True).

AI explanation

To verify the solution (b, a), substitute x = b and y = a into the first equation to get ba + ab = 2ab, which holds true. Substituting these values into the second equation yields (ba)^2 + (ab)^2 = 2b^2a^2, which simplifies to 2a^2b^2 = 2a^2b^2, proving that (b, a) is the correct solution.

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