Question

problem 2
drag the points to create a graph to determine ( x )- and ( y )-values that make both of the equations ( y = -\frac{2}{3}x + 3 ) and ( y = x - 2 ) true.
(graph with x-axis from -10 to 10, y-axis from -10 to 10, green and blue horizontal lines with points, and a submit button area)

Explanation:

Step1: Set equations equal

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

Step2: Solve for \( x \)

Add \( \frac{2}{3}x \) to both sides: \( 3 = \frac{5}{3}x - 2 \).
Add 2 to both sides: \( 5 = \frac{5}{3}x \).
Multiply by \( \frac{3}{5} \): \( x = 3 \).

Step3: Find \( y \)

Substitute \( x = 3 \) into \( y = x - 2 \): \( y = 3 - 2 = 1 \).

Answer:

The solution is \( x = 3 \) and \( y = 1 \), so the point is \( (3, 1) \).