Question 115431
Hello there,

1. x^2 - y^2 = 1 and x^2 + y = 7 

The easier method is actually elimination. 

If I subtract both equations, I get:

-y^2 - y = -6

-y^2 - y + 6 = 0

-(y^2 + y - 6)= 0

-(y + 3)(y - 2) = 0

y = -3, 2

Can you take it from here?

2. -x^4 + 15x^2 - 50 = 0 

Let y = x^2.

-y^2 + 15y - 50 = 0

y = 5, 10

Since y = x^2, you have the following two equations:

x^2 = 5 and x^2 = 10

If you square root both sides, you get {{{ x = sqrt(5) }}} and {{{ x = sqrt(10) }}}. If you want to check them, plug them into the original equation.

Hope this helps! Write back for more help!