Question

what is the approximate solution of this system of equations?
y = x² + 3x + 3
y = x² + x + 2

a. (-0.5, 0.2)
b. (-0.5, 1.7)
c. (-0.1, 1.2)
d. (0.2, 1.5)

Explanation:

Step1: Set equations equal

Since both equal \( y \), set \( x^2 + 3x + 3 = x^2 + x + 2 \).

Step2: Solve for \( x \)

Subtract \( x^2 \) from both sides: \( 3x + 3 = x + 2 \).
Subtract \( x \) and 3: \( 2x = -1 \), so \( x = -\frac{1}{2} = -0.5 \).

Step3: Find \( y \) (use one equation)

Plug \( x = -0.5 \) into \( y = x^2 + x + 2 \).
\( y = (-0.5)^2 + (-0.5) + 2 = 0.25 - 0.5 + 2 = 1.75 \approx 1.7 \).

Answer:

B. \((-0.5, 1.7)\)