Question

Please help:What are the solutions to the system of equations?y = 2x^2 − 4x + 1y = 4x + 1Enter your answers in the boxes. (__ , __ ) and ( __ , __)

Answer 1

Given the system of equations:

y = 2x² − 4x + 1 eq. 1

y = 4x + 1 eq. 2

First, we substitute the y value:

2x² − 4x + 1 = 4x + 1

Now we solve for x; as follows:

2x² − 4x + 1 - 4x - 1 = 0

2x² − 8x = 0

2x (x - 4) = 0

x₁ = 0

x₂ = 4

Now we substitute both values on equation 2:

y = 4x + 1

y₁ = 4(0) + 1

y₁ = 1

y₂ = 4(4) + 1

y₂ = 17

Solutions:

(0, 1) and (4, 17)