Question

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

Explanation:

Step1: Set equations equal

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

Step2: Solve for \( x \)

Subtract \( \frac{1}{3}x \) and 2: \( -\frac{4}{3}x-\frac{1}{3}x=2 - 2 \) → \( -\frac{5}{3}x = 0 \) → \( x = 0 \).

Step3: Find \( y \)

Substitute \( x = 0 \) into \( y=\frac{1}{3}x + 2 \): \( y=\frac{1}{3}(0)+2 = 2 \).

Answer:

The solution is \( (0, 2) \)