Hey, I just have two questions, Thanks.

Question

1. Find the exact solutions of x² - (y - 6)² = 36 and y = -x²

2. Solve the system,4x² + y² = 20 and y = 4x.

Answer 1

#1 since you know that y = -x^2, just plug that in:

x^2 - (-x^2-6)^2 = 36

This has no real solutions. If you graph the hyperbola and the parabola, you will see that they do not intersect.

http://www.wolframalpha.com/input/?i=plot+x%C2%B2+-+%28y+-+6%29%C2%B2+%3D+36+%2C+y+%3D+-x%C2%B2++where-10+%3C%3D+x+%3C%3D+10

#2 y=4x, so

4x² + (4x)² = 20
20x^2 = 20
x = ±1

http://www.wolframalpha.com/input/?i=plot+4x%C2%B2+%2B+y%C2%B2+%3D+20+%2C+y+%3D+4x

Answer 2

Thank you so much, that was very helpful:)