Question

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.
(3,1)
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Explanation:

Step1: Set the equations equal

To find the solution, set \(-\frac{2}{3}x + 3 = x - 2\) (since both equal \(y\)).

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 both sides by \(\frac{3}{5}\): \(x = 3\).

Step3: Find \(y\)

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

Answer:

\((3, 1)\)