Determine the number of solutions

Question

y=x^2-3

y=-2x+4

Help!

Answer 1

Substitute the second equation into the first.

-2x+4 = x^2 - 3

x^2 + 2x - 7 = 0

x = -1 ± 2√2

As y = -2x + 4, when x = -1 - 2√2, y = 6 + 4√2

when x = -1 + 2√2, y = 6 - 4√2

Our solutions are (-1 - 2√2, 6 + 4√2) and (-1 + 2√2, 6 - 4√2)