Which of the following systems of equations has the solution (-2, 1)?

Let's substitute (-2, 1) into each system of equations to see which one gives a true statement.

A. For 2x - y = -5:
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5

For x + 2y = 10:
-2 + 2(1) = 10
-2 + 2 = 10
0 = 10

Since both equations in system A do not hold true for (-2, 1), so A is not the correct system.

B. For x - 4y = 8:
-2 - 4(1) = 8
-2 - 4 = 8
-6 ≠ 8

For 3x + 10 = -2y:
3(-2) + 10 = -2(1)
-6 + 10 = -2
4 ≠ -2

Both equations in system B do not hold true for (-2, 1), so B is not the correct system.

C. For y = -2x - 2:
1 = -2(-2) - 2
1 = 4 - 2
1 = 2

For 2x - 2y = 5:
2(-2) - 2(1) = 5
-4 - 2 = 5
-6 ≠ 5

The equations y = -2x - 2 and 2x - 2y = 5 in system C do not have (-2, 1) as a solution.

D. For y = -3/2x - 2:
1 = -3/2(-2) - 2
1 = 3 + 2
1 = 5

For 2x - y = -5:
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5

The equations y = -3/2x - 2 and 2x - y = -5 in system D have (-2, 1) as the solution.

Therefore, the correct system of equations is D.