Question

solve the system of equations graphed on the coordinate axes below.
y = \frac{2}{3}x + 6
y = -3x + 6

Explanation:

Step1: Set the equations equal

Since both equations equal \( y \), set \( \frac{2}{3}x + 6 = -3x + 6 \).

Step2: Solve for \( x \)

Subtract 6 from both sides: \( \frac{2}{3}x = -3x \).
Add \( 3x \) to both sides: \( \frac{2}{3}x + 3x = 0 \).
Convert \( 3x \) to thirds: \( \frac{2}{3}x + \frac{9}{3}x = 0 \) → \( \frac{11}{3}x = 0 \).
Multiply both sides by \( \frac{3}{11} \): \( x = 0 \).

Step3: Find \( y \)

Substitute \( x = 0 \) into \( y = \frac{2}{3}x + 6 \): \( y = \frac{2}{3}(0) + 6 = 6 \).

Answer:

The solution is \( (0, 6) \)