Systems of Inequalities

The solution to a system of this type is the intersection of the regions corresponding to the solution of each inequality.

1. Represent the first inequality's solution region.

Transform the inequality into an equality.

2x + y = 3

Give two values to one of the two variables. This will create two points.

x = 0;     2 · 0 + y = 3;   y = 3;          (0, 3)

x = 1;     2 · 1 + y = 3;   y = 1;          (1, 1)

Join these two points to create a straight line and represent it graphically.

Take a point, for example (0, 0) and place these values into the inequality. If this inequality is true, the solution is the half plane where the point is on the graph, otherwise the solution will be the other half plane.

2x + y ≤ 3

2 · 0 + 0 ≤ 3       0 ≤ 3      Yes

2.Represent the second inequality's solution region.

x + y = 1

x = 0;      0 + y = 1;   y = 1;          (0, 1)

x = 1;      1 + y = 1;   y = 0;          (1, 0)

;

x + y ≥ 1

0 + 0 ≥ 1      No

3.The solution is the intersection of region's solutions.