# Systems of Linear Inequalities in Two Variable

**Outline**

2 Word problems and inequalities

3 Graphing systems of inequalities

**Problem
**Graph the following inequalities:

3x + 4y ≤ 24

3x + 4y > 12.

Follow these steps to graph the inequality 3x + 4y ≤ 24.

• Graph the line 3x + 4y = 24; the intercept method is
best for this

purpose.

• The plane has been divided into two halves , only one of
which

corresponds to the inequality .

• Determine which half to shade by analyzing a test point.
Since (0, 0)

satisfies the inequality , it is in the half to be shaded and we shade

accordingly.

• You can see these steps on the next slide.

**Example**

**Problem**

Fruit Punch A is 10% lemon juice. Fruit Punch B is 20%
lemon juice. If

you require at least 30 ounces of lemon juice each day, find a system of

inequalities that describes those combinations of punch which satisfy your

requirements.

Let a and b denote the number of ounces of punch A and B. Then

**Problem
**Graph the system of inequalities: 5x + 2y ≤ 20, x ≥ 0, and y ≥ 0. In

other words, find all points in the plane that simultaneously satisfy the set

of inequalities.

**Problem**

Graph the system of inequalities:

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