Solve algebraically
y=x^2 + 2x
y=3x+20

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 + ) / (2 a)

= (- (-1) + ) / (2 × 1)

= (1 + 9) / 2

= 10 / 2

= 5

and

x₂ = (-b - ) / (2 a)

= (1 - 9) / 2

= -4.

Find the value of y in both case.

y₁ = 3 × 5 + 20 = 35.

y₂ = 3 × (-4) + 20 = 8.

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