Solve the system of equations. y = x + 3 y = x2 − 2x − 1 A. (1,4) and (-4,-1) B. (-1,7) and (4,2) C. (-1,4) and (4,-1) D. (-1,2) and (4,7)

D

Step-by-step explanation:

Given the 2 equations

y = x + 3 → (1)

y = x² - 2x - 1 → (2)

Substitute y = x² - 2x - 1 into (1)

x² - 2x - 1 = x + 3 ← subtract x + 3 from both sides

x² - 3x - 4 = 0 ← in standard form

(x - 4)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 1 = 0 ⇒ x = - 1

Substitute these values into (1) for corresponding values of y

x = 4 ⇒ y = 4 + 3 = 7 ⇒ (4, 7 )

x = - 1 ⇒ y = - 1 + 3 = 2 ⇒ (- 1, 2 )

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^