Answer:
D
Step-by-step explanation:
Given the 2 equations
y = x - 5 → (1)
y = x² - 5x + 3 → (2)
Substitute y = x² - 5x + 3 into (1)
x² - 5x + 3 = x - 5 ← subtract x - 5 from both sides
x² - 6x + 8 = 0 ← in standard form
(x - 2)(x - 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 4 = 0 ⇒ x = 4
Substitute each of these values into (1) for corresponding values of y
x = 2 → y = 2 - 5 = - 3 ⇒ (2, - 3 )
x = 4 → y = 4 - 5 = - 1 ⇒ (4, - 1 )
Answer: (4, -1) and (2, -3) (D)
Step-by-step explanation:
From equation (1)
y = x- 5 ------------------- 1
y = x² -5x + 3 ------------2
Equate the 1 and 2 together since they are the same y, if plotted on the graph it is going to be quadratic and linear .
Now solve the two together becomes
x² - 5x + 3 = x - 5
x²- 5x - x + 3 + 5 = 0
x² - 6x + 8 =0
Solve using any method
x² - 2x - 4x + 8 =0
Here I used grouping methof
x(x - 2) - 4(x - 2) = 0
(x - 2)(x - 4) = 0
x = 2 or 4.
Now to find y,
Consider equation 1 by substitute for x
y = x - 5
When x = 2, y = 2 - 5
y = -3,
When x = 4, y = 4 - 5
y = -1
The coordinate
= (2, - 3) ; ( 4, -1)
Therefore the answer is D.
