vintage83 wrote:

If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

A. 0

B. 1

C. 2

D. 5

E. 10

This problem can still be easily solved without utilizing a "trick" in the algebra; you have two equations, just solve for x & y.

\(x + y = 2\)

\(y = x -2\)

\(x^2 - xy - 10 - 2y^2 = 0\)

\(x^2 - x(2-x) - 10 - 2(x^2 - 4x +4)\)

\(x^2 - 2x +x^2 - 10 - 2x^2 + 8x -8\)

Here, the quadratic conveniently cancels out, so we're left with a linear equation.

\(6x - 18 = 0,\)

\(x = 3.\)

Using x = 3 and our first equation, we have that y = -1, and thus that x - 2y = 3 - 2(-1) = 3+2 = 5.

Answer: D.