Question

Find all solutions of the system of equations algebraically. Write your solutions as coordinate points.

y = −3x² − 18x − 47
17 = 3x − y

Answer 1

(-2, -23) and (-5, -32)

Explanation:

17 = 3x - y

y = 3x - 17

Substitute y = 3x -17 into the 1st equation

y = −3x² − 18x − 47

3x - 17 = −3x² − 18x − 47

3x² + 21x + 30 = 0

x² + 7x + 10 = 0

(x + 2)(x + 5) = 0

x₁ = -2 → y₁ = 3(-2) - 17

= -23

x₂ = -5 → y₂ = 3(-5) - 17

= -32