Lesson 7.6 Solve Systems of Linear Inequalities

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Presentation transcript:

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

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

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

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.

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

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

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

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

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

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

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.

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?

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?

How do you solve a system of linear inequalities?

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