Section 7'6 Solving Systems of Linear Inequalities

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Section 7.6Solving Systems of Linear
Inequalities
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Graphing Linear Inequalities in Two Variables

• An ordered pair (x,y) is a solution to the
  inequality if the inequality holds true when the
  values of x and y are substituted.

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Graphing a Linear Inequality
Recall that we learned how to graph linear
inequalities in Chapter 4.
Step 1 Graph the corresponding equation.
Use a dotted line for inequalities with lt or gt
to show the points on the line are not solutions.

• Use a solid line for inequalities with a
• to show the points on the line
• are solutions.

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Graphing a Linear Inequality
Step 2 The line separates the coordinate plane
into two half-planes.
Test a point in one of the half-planes to find
out whether it is a solution of the inequality.
(We normally used point (0,0)).
Step 3 If the test point is a solution, shade
the half- plane it is in. Otherwise, shade in
the other half-plane.
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Example
Solve and graph the following inequality
x-int (3,0) y-int (0,3)
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Example
Solve and graph the following inequality
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Example
Solve and graph the following inequality
x-int (1/2, 0) y-int (0, -1)
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Example 1
Now we will use a similar process to solve a
system of linear inequalities through graphing.
Solve the following system of linear inequalities
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Example 1
The solution set is shaded green.
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Example 2
Solve the following system of linear inequalities
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Example 2
The solution set is shaded light blue.
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Example 3
Solve the following system of linear inequalities
First, solve the second equation for y
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Example 3
The solution set is shaded light blue.
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Example 4
Solve the following system of linear inequalities
First, solve each equation for y
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Example 4
The solution set is hatched in red.
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Example 5
What if there are more than two inequalities?
Solve the following system of linear inequalities
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Example 5(continued)
First, graph each equation separately.
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Example 5(continued)
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Example 5(continued)
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Example 5(continued)
Now, map the graphs of each equations together.
The solution set is shaded light blue.
The solution is the set of points that satisfies
each inequality.
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Example 6
Solve the following system of linear inequalities
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Example 6(continued)
The solution set is shaded light blue.