Solve the system y = -x + 7 and y = 0.5(x - 3)2

(5, 2 ) and (- 1, 8 )

Step-by-step explanation:

Given the equations

y = - x + 7 → (1)

y = 0.5(x - 3)²

   = 0.5(x² - 6x + 9)

y    = 0.5x² - 3x + 4.5 → (2)

Substitute y = - x + 7 into (2)

- x + 7 = 0.5x² - 3x + 4.5 ( subtract - x + 7 from both sides )

0 = 0.5x² - 2x - 2.5 ( multiply through by 2 ) , then

x² - 4x - 5 = 0 ← in standard form

(x - 5)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 1 = 0 ⇒ x = - 1

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

x = 5 : y = - 5 + 7 = 2 ⇒ (5, 2 )

x = - 1 : y = -(- 1) + 7 = 1 + 7 = 8 ⇒ (- 1, 8 )

∠cbe and ∠deb are same-side interior angles.

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