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

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

Step-by-step explanation:

Given the 2 equations

y = - x + 7 → (1)

y = 0.5(x - 3)² → (2)

Substitute y = 0.5(x - 3)² into (1)

0.5(x - 3 )² = - x + 7 ← expand and simplify left side

0.5(x² - 6x + 9) = - x + 7 ( multiply both sides by 2 )

x² - 6x + 9 = - 2x + 14 ( subtract - 2x + 14 from both sides )

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 = 8 ⇒ (- 1, 8 )

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