Multiple choice

Solve the following system of equations. $(a-b)x+(a+b)y=a^2-2ab-b^2$, $(a+b)(x+y)=a^2+b^2$.

  1. $a-b, -2ab$
  2. $a+b, -2ab$
  3. $a^2+b^2, \displaystyle\frac{-2ab}{a+b}$
  4. $a+b, \displaystyle\frac{-2ab}{a+b}$
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D Correct answer
AI explanation

From the second equation, (a + b)(x + y) = a^2 + b^2, we get x + y = (a^2 + b^2) / (a + b). Substituting y = [(a^2 + b^2) / (a + b)] - x into the first equation and simplifying yields x = a + b. Substituting this value of x back into the expression for y gives y = (a^2 + b^2) / (a + b) - (a + b), which simplifies to y = -2ab / (a + b). Therefore, the solution is x = a + b and y = -2ab / (a + b).

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