Solve the system of equations: y = 3x – 5 and y = x² – 5

(1 point)
A) (5, 0) and (4, 3)
B) (–5, 0) and (3, 4)
C) (0, 5) and (4, 3)
D) (0, –5) and (3, 4)

1 answer

To solve this system of equations, we can set the right sides of the equations equal to each other:

3x – 5 = x² – 5

Now, let's move all terms to the left side of the equation:

x² - 3x + 5 - 5 = 0

Simplifying:

x² - 3x = 0

Factor the equation:

x(x - 3) = 0

Now we have two possible solutions for x:

x = 0 or x - 3 = 0

If x = 0, substituting into one of the original equations:

y = 3(0) - 5

y = -5

Therefore, one solution is (0, -5).

If x - 3 = 0, solving for x:

x = 3

Substituting into one of the original equations:

y = 3(3) - 5

y = 4

Therefore, another solution is (3, 4).

The correct answer is D) (0, –5) and (3, 4).