Question

How many solutions does the following system have?

Y = 8x - 6
(y = 2x² - 16x + 36)
a) One solution
b) Two solutions
c) No solution
d) Infinite solutions

Answer 1

The system of equations has two solutions.

Step-by-step explanation:

To determine how many solutions the system of equations has, we need to solve the equations and examine the results.

Given:

y = 8x - 6

y = 2x² - 16x + 36

To find the solution, we can set the two equations equal to each other:

8x - 6 = 2x² - 16x + 36

Now, we have a quadratic equation. We can rearrange it to standard form:

2x² - 24x + 42 = 0

Using the quadratic formula, we can find the discriminant:

Discriminant = b² - 4ac = (-24)² - 4(2)(42)

Discriminant = 576 - 336 = 240

Since the discriminant is positive, the quadratic equation has two distinct real roots. So, the system of equations has two solutions (b).