What is meant by a system of inequalities?

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Answer 1 · 2015-08-29T20:50:35

A system of inequalities is a set of inequalities that you deal with all at once.

Solving a system of inequalities means graphing each individual inequality and then finding the overlaps of the various solutions.

EXAMPLE:

Solve the following system:

#2x – 3y ≤ 12#
#x + 5y ≤ 20#
#x > 0#

Solution:

Step 1: Solve as many of the inequalities as possible for #y#.

#y ≥ 2/3x – 4#
#y ≤ – 1/5 x + 4#
#x > 0#

Step 2. Graph each inequality, shading the area that satisfies the condition.

(a) Graph #y ≥ 2/3x – 4#

Graph1

(b) Graph #y ≤ – 1/5x + 4#

Graph2

(c) Graph #x>0#

This is a ">" inequality, so you use a dashed line to show that #x=0# is not part of the solution.

Graph3

(d) Shade the area that satisfies all the inequalities.

Graph4

And you have solved your system of inequalities.