unit 2: solving systems of equations
DESCRIPTION
Unit 2: Solving Systems of Equations. Key Ideas. Reasoning with Equations & Inequalities. Understanding how to solve equations Solve equations and inequalities in one variable Solve systems of equations Represent and solve equations and inequalities graphically. Example. - PowerPoint PPT PresentationTRANSCRIPT
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Unit 2: Solving Systems of Equations
Key Ideas
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Reasoning with Equations & Inequalities
• Understanding how to solve equations
• Solve equations and inequalities in one variable
• Solve systems of equations• Represent and solve equations and
inequalities graphically.
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ExampleSolve the equation 8(x + 2) = 2(y + 4) for y.
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ExampleSolve the equation 8(x + 2) = 2(y + 4) for y.
8x + 16 = 2y + 88x + 8 = 2y4x + 4 = y
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ExampleKarla wants to save up for a prom dress.
She figures she can save $9 each week from the money she earns babysitting.
If she plans to spend up to $150 for the dress, how many weeks will it take her to save enough money?
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ExampleKarla wants to save up for a prom dress. She figures she can save $9 each week from the money she earns babysitting. 9xIf she plans to spend up to $150 for the dress, how many weeks will it take her to save enough money? ≤ 150
9x ≤ 150x ≤ 16.67 ≈ 17 weeks
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Example• This equation can be used to find
h, the number of hours it takes Bill and Bob to clean their rooms.
• How many hours will it take them?
15 20h h
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Example• This equation can be used to find
h, the number of hours it takes Bill and Bob to clean their rooms.
• How many hours will it take them? 4
15 20h h
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Example• You are selling tickets for a
basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450.
• Use a system of linear equations
to determine how many student tickets you sold?
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Example• You are selling tickets for a
basketball game. Student tickets (s) cost $3 and general admission (g) tickets cost $5. You sell 350 tickets and collect $1450. • Use a system of linear equations
to determine how many student tickets you sold? s + g = 350
3s + 5g = 1450I sold 150 student tickets
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ExampleYou sold 52 boxes of candy for a fundraiser. The large size box sold for $3.50 each and the small size box sold for $1.75 each. If you raised $112.00, how many boxes of each size did you sell?
A. 40 large, 12 smallB. 12 large, 40 smallC. 28 large, 24 smallD. 24 large, 28 small
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ExampleYou sold 52 boxes of candy for a fundraiser. The large size (l) box sold for $3.50 each and the small size (s) box sold for $1.75 each. If you raised $112.00, how many boxes of each size did you sell? l + s = 52
3.5l + 1.75s = 112A. 40 large, 12 smallB. 12 large, 40 smallC. 28 large, 24 smallD. 24 large, 28 small
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ExampleYou sold 61 orders of frozen pizza for a fundraiser. The large size sold for $12 each and the small size sold for $9 each. If you raised $660.00, how many of each size did you sell?
A. 24 large, 37 smallB. 27 large, 34 smallC. 34 large, 27 smallD. 37 large, 24 small
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ExampleYou sold 61 orders of frozen pizza for a fundraiser. The large size (l) sold for $12 each and the small size (s) sold for $9 each. If you raised $660.00, how many of each size did you sell? l + s = 61
12l + 9s = 660
A. 24 large, 37 smallB. 27 large, 34 smallC. 34 large, 27 smallD. 37 large, 24 small
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Example Which equation corresponds to the graph shown?• A. y = x + 1• B. y = 2x + 1• C. y = x – 2• D. y = 3x
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Example Which equation corresponds to the graph shown?• A. y = x + 1• B. y = 2x + 1• C. y = x – 2• D. y = 3x
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ExampleWhich graph would represent a system of linear equations that has no common coordinate pairs?
A B
C D
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ExampleWhich graph would represent a system of linear equations that has no common coordinate pairs?
A B
C D