Question

Find all points of intersection algebraically.
x - y - 1 = 0
y = x^2 - x - 1

Answer 1

x - x^2 - x - 1 - 1 = 0

Answer 2

-x^2 - 2 = 0

Answer 3

What do I do from there?

Answer 4

I solve the first equation for y, and I get this:
\[y = x - 1\]
then I replace y with x-1 into the second equation, so I can write:
\[x - 1 = {x^2} - x - 1\]
and after a simplification, I get this:
\[{x^2} - 2x = 0\]

Answer 5

That can be factored to x(x-2) = 0
Therefore x=0 and x=2 ?

Answer 6

correct!

Answer 7

Thank you very much!

Answer 8

:)