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Graphing Systems of Equations and Inequalities January 9, 2013
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Notes Setup Standards 9.0 Students solve a system of two linear equations or linear inequalities and are able to interpret them graphically 6.0 Sketch the region defined by a linear inequality Toolbox System of equations System of inequalities Consistent Independent Dependent Inconsistent Half-plane Boundary
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GRAPHING INEQUALITIES IN TWO VARIABLES Section 6-7:
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Get Ready for the Lesson Hannah budgets $30 a month for lunch. On most days, she brings her lunch. She can also buy her lunch at the cafeteria or at a fast food restaurant. She spends an average of $3 for lunch at the cafeteria and an average of $4 for lunch at the restaurant. How many times a month can Hannah buy her lunch and remain within her budget.
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Solution There are many solutions for this inequality. Each solution represents a different combination of lunches bought in the cafeteria and the restaurant.
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Graphing Linear Inequalities The solution set for an inequality in two variables contains many ordered pairs when the domain and range are a set of numbers.
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Graphing Linear Inequalities The graphs of these ordered pairs fill a region on the coordinate plane called a half- plane. An equation defines the boundary or edge of each half-plane.
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Graph the following:
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Real World Example Neil wants to run a marathon at a pace of at least 6 miles per hour. Write an inequality for the miles y he will run in x hours and graph the solution set.
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Answer
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More Practice P. 337 #’s 1 – 7
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Graphing Systems of Equations System of Equations: two or more equations together Consistent: if the graphs intersect (or coincide at one point); it has exactly one ordered pair to satisfy both equations Independent: it has exactly one solution Dependent: it has an infinite number of solutions Inconsistent: the graphs are parallel; there are no ordered pairs that satisfy both
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Example #1
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Answers to Example #1 1.One 2.No solution 3.Infinitely many 4.One
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Example #2 Graph Each System of Equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If it has one solution, name it.
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Answers to Example #2a
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Answer to #2b INFINITELY MANY
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Example #3
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Example #3 Continued 1.Write the equation for each equation 2.Graph each equation: y = 3x + 418 y = 8x + 309 3. Look for the intersection (22,485) Based on the information, both will be the same 22 years after 2004, or 2026
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Your Turn
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Answer Border: P=60 w= 2/3 length length 2 l + 2 w = 60 w = 2/3 l Now write each equation in terms of l and w w = 2/3 l w = ̶ l + 30
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Answer continued (18, 12) There are 18 bricks along one edge and 12 bricks along the other.
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Your Turn The length of the rectangle is 1 meter less than twice its width. What are the dimensions of the rectangle?
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Answer
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Summary: Pretend you are explaining how to graph inequalities to a friend. Explain all the steps needed to complete a problem. When solving a system of equations by graphing, how do we find the answer?
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Homework: P. 256 #’s 17-27 odd, 34-36, 40 P. 337-338 #’s 9-17 odd, 20-22, 27-30, 35, 36
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