Expert: Paul Klarreich - 3/16/2009

Question
Hi there Im really stuck with a maths problem.

Its a quadratic simultaneous equation. The equations are x² - y² = -5 and 2x² + xy -y² = 5

Thanks

Answer
Questioner:   Harry
Category:  Advanced Math
Private:  No
 
Subject:  Quadratic Simultaneous Equation
Question:  Hi there Im really stuck with a maths problem.

Its a quadratic simultaneous equation. The equations are x² - y² = -5 and 2x² + xy -y² = 5

Thanks
........................................
Here are your equations: (I can't make those cute square's.)

x^2 - y^2 = -5
2x^2 + xy - y^2 = 5

Factor each left side:

(x + y )(x - y) = -5
(2x - y)(x + y) = 5

Divide the left sides and right sides; (x+y)'s cancel and we have:

x - y
------ = - 1
2x - y

x - y = y - 2x  << multiply out

3x = 2y     << combine

y = 3x/2    << solve for y  [you could solve for x if you like.]


x^2 - (3x/2)^2 = -5   << put 3x/2  for y in the first eq.

x^2 - 9x^2/4 = -5

- 5x^2/4 = -5

  x^2/4 = 1

x = +- 2

y = +- 3