How many real solutions exist for this system of equations?

y = x2 + 4

y = 4x

A. zero

B. one

C. two

D. infinite

Guest Apr 14, 2023

#1**0 **

*How many real solutions exist for this system of equations?*

*y = x2 + 4*

*y = 4x*

* A. zero*

* B. one*

* C. two*

* D. infinite*

Assuming that x2 means x^{2}....

Since they both equal y, we can set x^{2} + 4 = 4x

Subtracting 4x from boths sides we get x^{2} - 4x + 4 = 0

This is a quadratic which will factor to (x - 2)(x - 2) = 0

Now here's where language gets tricky.

A quadratic has two solutions, but in this case __both__ solutions are x = 2.

So, is that considered one solution or two? I'd say **one**, because the curve touches zero at only one point, but semantics might determine what it is supposed to be called. I don't know if mathematics has a conventional nomenclature for this.

**.**

Guest Apr 14, 2023