Question

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Explanation:

Step1: Set equations equal

Since at intersection, \( y \) values are equal, set \( -\frac{1}{3}x + 7=\frac{2}{3}x + 1 \).

Step2: Solve for \( x \)

Add \( \frac{1}{3}x \) to both sides: \( 7=\frac{2}{3}x+\frac{1}{3}x + 1 \). Simplify: \( 7 = x + 1 \). Subtract 1: \( x = 6 \).

Step3: Find \( y \)

Substitute \( x = 6 \) into \( y = -\frac{1}{3}x + 7 \): \( y = -\frac{1}{3}(6)+7=-2 + 7 = 5 \).

Answer:

\( (6, 5) \)