Question

Which ordered pair is the solution to the system of equations `y=x` and `y=x^2-2`?

Answer 1

`(x, y) = (2, 2) " "` or `" " (x, y) = (-1, -1)`

Explanation:

If the first equation is satisfied then we can replace `y` with `x` in the second equation to get:

`x = x^2-2`

Subtract `x` from both sides to get the quadratic:

`0 = x^2-x-2 = (x-2)(x+1)`

Hence solutions `x=2` and `x=-1`.

To make each of these into ordered pair soltuions of the original system, use the first equation again to note that `y = x`.

So the ordered pair solutions to the original system are:

`(2, 2) " "` and `" " (-1, -1)`