Question

4.4.2 test (cst): systems of equations and inequalities
what is the solution to the system of equations graphed below?
graph of two lines: y = x + 2 and y = -2x - 4 intersecting

\\( y = -2x - 4 \\)
\\( y = x + 2 \\)

a. (0, 2)
b. (0, -2)
c. (2, 0)
d. (-2, 0)

Explanation:

Step1: Set the equations equal

Since \( y = x + 2 \) and \( y = -2x - 4 \), we set \( x + 2=-2x - 4 \).

Step2: Solve for x

Add \( 2x \) to both sides: \( x + 2x+ 2=-2x+ 2x - 4 \), so \( 3x + 2=-4 \).
Subtract 2 from both sides: \( 3x + 2 - 2=-4 - 2 \), so \( 3x=-6 \).
Divide by 3: \( x=\frac{-6}{3}=-2 \).

Step3: Find y

Substitute \( x = -2 \) into \( y = x + 2 \): \( y=-2 + 2 = 0 \).

Answer:

D. \((-2, 0)\)