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).
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