Question

Find all solutions of the system of equations algebraicllally. Write your solutions as coordinate points Y=3x^2- 2x-1 2x+y=11

Answer 1

(- 2, 15 ) and (2, 7 )

Explanation:

Given the 2 equations

y = 3x² - 2x - 1 → (1)

2x + y = 11 → (2) ← subtract 2x from both sides

y = 11 - 2x → (3)

Substitute y = 3x² - 2x - 1 into (3)

3x² - 2x - 1 = 11 - 2x ( subtract 11 - 2x from both sides )

3x² - 12 = 0 ( add 12 to both sides )

3x² = 12 ( divide both sides by 3 )

x² = 4 ( take the square root of both sides )

x = ±
`√(4)` = ± 2

Substitute these values into (3) for corresponding values of y

x = - 2 : y = 11 - 2(- 2) = 11 + 4 = 15 ⇒ (- 2, 15 )

x = 2 : y = 11 - 2(2) = 11 - 4 = 7 ⇒ (2, 7 )