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  a.  all points are part of the solution set

  b.  no points are in the solution set

Step-by-step explanation:

Graphs of the two systems of inequalities are attached.

a) The red area on the graph is the solution. The two inequalities can be combined to one compound inequality:

  x -1 < y < -1/2x +2

The two boundary lines intersect at x-1 = -1/2x +2   ⇒   x = 2, so there are no points in the solution set with x-values of 2 or greater.

All of the given points are in the solution set.

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b) The green area of the graph is the solution. Solving each inequality for y gives ...

  x -2y ≥ 4  ⇒  1/2x -2 ≥ y

  2x -y ≥ -1  ⇒  2x +1 ≥ y

The allowed values of y must be less than or equal to the minimum of these limits. The limits have the same value at 1/2x -2 = 2x +1   ⇒   x = -2, so the solution set is the area below and right of that intersection point of the two boundary lines.

None of the given points are in the solution set.

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right