How many solutions of the system x - y = 3 and x^2 - y = 1 are there such that both x and y are real?

Guest Sep 8, 2021

#1**0 **

*How many solutions of the system x - y = 3 and x^2 - y = 1 are there such that both x and y are real?*

Let's rearrange the two equations

Rearrange x – y = 3 to y = x – 3

Rearrange x^{2} – y = 1 to y = x^{2} – 1

The answer to "How many..." is **NONE**.

I graphed both equations on Desmos. I tried to paste in a screenshot of the curves, but couldn't figure out how.

y = x^{2} – 1 is an upward opening parabola that crosses the y-axis at (0,–1)

y = x – 3 is a straight line that passes beneath the parabola and crosses the y-axis at (0,–3)

The two curves never intersect each other, so they have no solutions in common.

**.**

Guest Sep 9, 2021

edited by
Guest
Sep 9, 2021