Graphing and solving systems of linear inequalities

Solutions of a system of linear inequalities A solution of a system of linear inequalities

is an ordered pair that is a solution of each inequality in the system.

(3, -1) is a solution to the system

x + y < 6

2x –y >4

since we get a true statement when we substitute 3 for x and -1 for y in both of the inequalities.

Graphing a system of linear inequalities

To graph a system of linear inequalities do the following for each inequality in the system.

Graph the line that corresponds to the inequality. Use a dashed line for an inequality with greater than or less than and a solid line for an inequality with greater than or equal to or less than or equal to.

Graphing a system of linear inequalities (continued) Lightly shade the half-plane that is the

graph of the inequality. Colored pencils may help you distinguish the different half planes.

The graph of the system is the region common to all of the half-planes. If you use colored pencils, it is the region that has been shaded with every color.

Graph the following system of linear inequalities

22

32

xy

xy

43

52

yx

yx

Sample problems

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