Question

which point satisfies the system of equations $y = 3x - 2$ and $y = -2x + 3$?

Explanation:

Step1: Solve the system of equations

We have the system:

$$
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$$

Set the two equations equal to each other: \(3x - 2=-2x + 3\)
Add \(2x\) to both sides: \(3x+2x - 2=-2x+2x + 3\) which simplifies to \(5x - 2 = 3\)
Add 2 to both sides: \(5x-2 + 2=3 + 2\) so \(5x=5\)
Divide both sides by 5: \(x = 1\)
Substitute \(x = 1\) into \(y = 3x - 2\): \(y=3(1)-2=1\)
So the solution is the point \((1,1)\), which is point D.

Step2: Verify with the graph

Looking at the graph, point D is at \((1,1)\), which matches the solution we found algebraically.

Answer:

D (the point at (1, 1))