Question

if the system of equations $y = 3x - 2$ and $y = -x + 6$ is graphed, at what point do the lines intersect?
(4,2)
(1,1)
(2,4)
(2,2)

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), set \( 3x - 2 = -x + 6 \).

Step2: Solve for \( x \)

Add \( x \) to both sides: \( 3x + x - 2 = 6 \) → \( 4x - 2 = 6 \).
Add 2 to both sides: \( 4x = 6 + 2 \) → \( 4x = 8 \).
Divide by 4: \( x = \frac{8}{4} = 2 \).

Step3: Find \( y \) using \( x = 2 \)

Substitute \( x = 2 \) into \( y = 3x - 2 \): \( y = 3(2) - 2 = 6 - 2 = 4 \).

Answer:

\((2, 4)\)