Answer:
x = 5 and y = 35
OR
x = -4 and y = 8.
Step-by-step explanation:
Equate the right-hand side of the two equations:
x² + 2 x = y = 3 x + 20.
x² + 2 x - 3 x - 20 = 0.
x² - x - 20 = 0.
Quadratic discriminant
Δ = b² - 4 a · c
= (-1)² - 4 × 1 × (-20)
= 81.
There are two roots:
x₁ = (-b + [tex]\sqrt{\Delta}[/tex]) / (2 a)
= (- (-1) + [tex]\sqrt{81}[/tex]) / (2 × 1)
= (1 + 9) / 2
= 10 / 2
= 5
and
x₂ = (-b - [tex]\sqrt{\Delta}[/tex]) / (2 a)
= (1 - 9) / 2
= -4.
Find the value of y in both case.
y₁ = 3 × 5 + 20 = 35.
y₂ = 3 × (-4) + 20 = 8.
