How many real solutions exist for this system of equations?

Question

y = x² + 4

y = 4x

A. 

zero

B. 

one

C. 

two

D. 

infinite

Answer 1

The "solutions" are (x, y) points where the "x" and "y" work in both equations. Therefore the "y" value in "y = x² + 4" must be the same as the "y" value in "y = 4x". So, since the "y" values are equal, the two right hand portions of the equations are also equal:

x² + 4 = 4x

x² - 4x + 4 = 0

(x - 2)(x - 2) = 0

x = 2

Since x = 2 and y = 4x, then y = 8 meaning the point (2, 8) is the one and only solution.