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Lesson 7.6 Solve Systems of Linear Inequalities

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1 Lesson 7.6 Solve Systems of Linear Inequalities
Essential Question: How do you solve systems of linear inequalities in two variables?

2 Before we start… Graph 𝑦=2π‘₯+1 and 𝑦=βˆ’π‘₯+2 in the same coordinate plane. Plot the point βˆ’2,3 . Shade the region bounded by the two lines that contains the point. Turn the equations into inequalities.

3 What is a system of linear inequalities?
It consists of two or more linear inequalities in the same variables.

4 What is a solution of a system of linear inequalities?
An ordered pair that is a solution of each inequality in the system. The graph of a system of linear inequalities is the graph of all solutions of the system.

5 Tell whether the ordered pair is a solution of the system of inequalities.

6 Tell whether the ordered pair is a solution of the system of inequalities.

7 Tell whether the ordered pair is a solution of the system of inequalities.

8 Tell whether the ordered pair is a solution of the system of inequalities.

9 Tell whether the ordered pair is a solution of the system of inequalities.

10 Tell whether the ordered pair is a solution of the system of inequalities.

11 How do you solve systems of linear inequalities in two variables?
Graph each inequality in the system. Using a different color for each inequality may be helpful. Identify the region that is common to all the graphs of the inequalities. This is the solution of the system.

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19 Ordering Cups You work at an Italian ice shop during the summer
Ordering Cups You work at an Italian ice shop during the summer. You need to order 5-ounce and 8-ounce cups. The storage room will only hold 10 more boxes of cups. A box of 5-ounce cups costs $15 and a box of 8-ounce cups costs $18. A maximum of $90 is budgeted for cups. What are possible combinations of cups you can buy?

20 Studying You need at least 4 hours to do your science and history homework. It is 1:00 P.M. on Sunday and your friend wants you to go to the movies at 7:00 P.M. How many hours can you spend working on each subject if you go to the movies?

21 How do you solve a system of linear inequalities?

22 Ticket Out the Door Is the ordered pair a solution of the system of linear inequalities?


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