Question

Solve the system by substitution or elimination.

x^2 + 2y^2 = 8
x^2 - y^2 = 1

Answer 1

subtract the equations to get

3y^2 = 7
y = ±√(7/3)
so,
x^2 - 7/3 = 1
x^2 = 10/3
x = ±√(10/3)

Answer 2

I'm sure you'd have had no trouble if it were

x+2y=8
x-y=1

Answer 3

Thank you! I tried to solve it like this:

x^2 + 2y^2 = 8
( x^2 - y^2 = 1 )2

x^2 + 2y^2 = 8
2x^2 - 2y^2 = 2

3x^2 = 10
x^2 = 10/3
x = ±√(10/3)

Any idea as to why my textbook would say that the solution is ±√(30/3)?

Answer 4

I figured it out. No fraction can appear under a radical.

Answer 5

Check the bracket placement.

±√(10/3)
= ±√(10)/√(3)
= ±√(30)/3
= ±(⅓)√(30)

Answer 6

Yeah, lots of folks don't like to see radicals in the denominator. Pretty much a non-issue with me, but since it's a common practice, be sure to watch for it.