Question

select the correct answer.
solve the system of equations.
y = x - 5
y = x² - 5x + 3
a. (4,-1) and (2,-3)
b. (-4,-9) and (-2,-7)
c. (4,-9) and (2,-7)
d. (4,-3) and (2,-1)

Explanation:

Step1: Set the equations equal

Since both equal \( y \), set \( x - 5 = x^2 - 5x + 3 \).

Step2: Rearrange into quadratic

\( x^2 - 6x + 8 = 0 \).

Step3: Factor the quadratic

\( (x - 4)(x - 2) = 0 \), so \( x = 4 \) or \( x = 2 \).

Step4: Find corresponding \( y \)

For \( x = 4 \), \( y = 4 - 5 = -1 \). For \( x = 2 \), \( y = 2 - 5 = -3 \).

Answer:

A. (4,-1) and (2,-3)