Question

select the correct answer.
what is the solution set of this system?
y = 4x
2x² - y = 0
a. (-1.5, -2) and (2, 8)
b. (1.5, 2) and (8, 2)
c. (0, 0) and (2, 8)
d. (0.5, 0.5) and (2, -8)

Explanation:

Step1: Substitute $y=4x$ into quadratic equation

$2x^2 - 4x = 0$

Step2: Factor the equation

$2x(x - 2) = 0$

Step3: Solve for $x$ values

$2x=0 \implies x=0$; $x-2=0 \implies x=2$

Step4: Find corresponding $y$ values

For $x=0$: $y=4(0)=0$; For $x=2$: $y=4(2)=8$

Answer:

C. $(0, 0)$ and $(2, 8)$