Question

What is meant by a system of inequalities?

Answer 1

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

Explanation:

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`

(b) Graph `y ≤ – 1/5x + 4`

(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.

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

And you have solved your system of inequalities.