Question

solve the system of equations graphed on the coordinate axes below.
$y = \frac{1}{3}x + 7$
$y = -\frac{2}{3}x + 4$

Explanation:

Step1: Set the equations equal

Since both equal \( y \), set \( \frac{1}{3}x + 7 = -\frac{2}{3}x + 4 \).

Step2: Solve for \( x \)

Add \( \frac{2}{3}x \) to both sides: \( \frac{1}{3}x + \frac{2}{3}x + 7 = 4 \), which simplifies to \( x + 7 = 4 \). Subtract 7: \( x = 4 - 7 = -3 \).

Step3: Find \( y \)

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

Answer:

The solution is \( x = -3 \), \( y = 6 \) (or the ordered pair \((-3, 6)\)).