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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