# How do you determine the solution in terms of a system of linear equations for 5x^2+y^2 = 14, 3x^2 -2y^2 = -15?

Sep 25, 2015

$x = \pm 1 , y = \pm 3$

#### Explanation:

Write ${x}^{2} = X , {y}^{2} = Y$, which would make it a system of linear equations.
5X+Y=14 and 3X-2Y= -15. This can be solved by substituting Y= 14-5X in 3X-2Y= -15 as,

3X -2(14-5X)=-15
13X= 28-15=13. giving X=1 and then having Y=14-5=9

X=1 and Y=9 would mean $x = \pm 1 , y = \pm 3$