Question

How many solutions does the following system have?

Y=2x2−18x+45
y=2x−5
a) 0
b) 1
c) 2
d) Infinite

Answer 1

The given system of equations has 1 solution.

Step-by-step explanation:

The given system of equations is:

Y = 2x^2 - 18x + 45

y = 2x - 5

To determine the number of solutions, we need to find the points of intersection between the two equations. We can do this by setting the two equations equal to each other:

2x^2 - 18x + 45 = 2x - 5

Simplifying the equation, we get:

2x^2 - 20x + 50 = 0

This is a quadratic equation. We can use the discriminant to determine the number of solutions. The discriminant is given by:

Discriminant = b^2 - 4ac

In this case, a = 2, b = -20, and c = 50. Plugging in the values, we get:

Discriminant = (-20)^2 - 4(2)(50)

Discriminant = 400 - 400

Discriminant = 0

Since the discriminant is zero, the quadratic equation has 1 solution. Therefore, the given system of equations has 1 solution.