Question

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`?

Answer 1

`x=+-1, y= +-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=+-1, y= +-3`