Algebra 2/Trig Name: ____________________________________
p. 179
VOCABULARY:
System of linear inequalities - A system of two or more linear inequalities in two variables
Solution of a system of linear inequalities - An ordered pair that is a solution of each inequality in the system
Graph of a system of linear inequalities -The graph of all solutions of the system
GRAPHING A SYSTEM OF LINEAR INEQUALITIES
To graph a system of linear inequalities, follow these steps:
Step 1 : Graph each inequality in the system. You may want to use colored pencils to distinguish the different half-planes.
Step 2 : Identify the region that is common to all the graphs of the inequalities. If you used colored pencils, the graph of the system is the region that has been shaded with every color.
𝑦 < 2𝑥 + 1
Example 1 : Graph the system. {
𝑦 ≤ −𝑥 − 3
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Example 2: Graph the system. { 𝑥 ≥ 0 𝑦 ≥ 0 𝑦 < −𝑥 + 2
𝑦 ≥ −2𝑥 + 3
Find the coordinates of the veritices.
Do the coordinates of the vertices in the graph satisfy the system? 𝑦 > −𝑥 − 2
Example 3: Graph the system of inequalities. { 𝑦 < −5𝑥 + 2 𝑥 ≤ −1
What are the vertices of the feasible region?
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Example 4: Graph the system of inequalities. {
𝑦 > −𝑥 − 2
𝑦 ≤ 2𝑥 + 1 𝑦 ≤ 3
Identify the vertices. Give a solution.
Example 5: Graph the inequality. 1 ≤ 𝑦 < 4
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Example 6: Write a system of linear inequalities for the shaded region. b.) a.)
Example 7:
For an upcoming event, a 2500 seat arena is selling tickets for $25 and $15. At least 1000 tickets must be priced at $15 and total sales need to exceed $10, 000 to make a profit. Let x represent the number of tickets priced at $25 and y represent the number of tickets priced at $ 15. Write a system of inequalities that shows the possible combinations of ticket sales in order to make a profit.
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Homework: Page 183 – 185. #12 – 44 FOURTHS, (12, 16, 20, 24, etc) AND 48 – 52 ALL
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