Question

question 19 of 25
what is the solution to the system of equations graphed below?
graph with two lines: y = x + 2 (blue) and y = 3x - 2 (red)
click here for long description

y = x + 2
y = 3x - 2

a. (4, 2)
b. (0, 2)
c. (2, 4)
d. (0, -2)

Explanation:

Step1: Set the equations equal

Since \( y = x + 2 \) and \( y = 3x - 2 \), we set \( x + 2 = 3x - 2 \).

Step2: Solve for x

Subtract \( x \) from both sides: \( 2 = 2x - 2 \).
Add 2 to both sides: \( 4 = 2x \).
Divide by 2: \( x = 2 \).

Step3: Find y

Substitute \( x = 2 \) into \( y = x + 2 \): \( y = 2 + 2 = 4 \).

Answer:

C. (2, 4)