Final answer:
The point that satisfies the system of equations y = 3x - 2 and y = -2x + 3 is found by setting the two equations equal to each other, solving for x, and then finding y using the found value of x. The coordinates of the satisfying point are (1, 1).
Step-by-step explanation:
To find which point satisfies the system of equations given by y = 3x - 2 and y = -2x + 3, we can set the two equations equal to each other since they both equal y. Therefore, we have:
3x - 2 = -2x + 3.
To solve for x, we add 2x to both sides and add 2 to both sides:
3x + 2x = 3 + 2
5x = 5
Now, divide both sides by 5 to get:
x = 1
Now that we have the value of x, we can plug it into either of the original equations to find the value of y. Let's use the first equation:
y = 3(1) - 2
y = 3 - 2
y = 1
So the point that satisfies both equations is (1, 1). Without the coordinates being provided as options (like A, B, C, D), we can't directly associate this point to one of them. However, the coordinates of the point that satisfies both equations are (1, 1).