Given the system of equations y = 2x^2 and y = 2x, which statement is true?

To analyze the system of equations given by y = 2x² and y = 2x, we start by setting both expressions for y equal to each other:

2x² = 2x

Next, we can simplify this equation by dividing both sides by 2 (assuming x is not zero):

x² = x

Rearranging this gives us:

x² – x = 0

Factoring out x from the equation, we have:

x(x – 1) = 0

This implies:

• x = 0
• x = 1

To find the corresponding values of y, we can substitute these values of x back into either of the original equations. Let’s use y = 2x:

• For x = 0: y = 2(0) = 0
• For x = 1: y = 2(1) = 2

Thus, the points of intersection for the system of equations are:

• (0, 0)
• (1, 2)

Both points represent solutions to the system, meaning that the correct statement regarding the system of equations is that it has two points of intersection at (0, 0) and (1, 2).