Answer:
Explanation:
The only point that lies on both lines y = - 1/2x + 2 and y = 1/2x - 3 is **(-1/2, 5)**. So the answer is **C**.
To see this, we can substitute the x-coordinate of (-1/2, 5) into each equation. If we substitute x = -1/2 into the first equation, we get y = -1/2 * (-1/2) + 2 = 1/2 + 2 = 5. If we substitute x = -1/2 into the second equation, we get y = 1/2 * (-1/2) - 3 = -1/4 - 3 = -5/4.
Since both equations give us the same y-coordinate, (-1/2, 5) must lie on both lines.
The other points do not lie on both lines. For example, if we substitute x = 5 into the first equation, we get y = -1/2 * 5 + 2 = -2.5 + 2 = -0.5. However, if we substitute x = 5 into the second equation, we get y = 1/2 * 5 - 3 = 2.5 - 3 = -0.5. This shows that (5, -1/2) does not lie on either line.
Similarly, the other points do not lie on both lines. Therefore, the only point that lies on both lines is (-1/2, 5), and the answer is **C**.