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Published byLeah Poole Modified over 2 years ago

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Warm-Up 5 minutes Write each equation in slope-intercept form. 1) x – y = 9 2) 2x = 5y 3) 4x + 7y = 14 4) 5)

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3.1.1 Solving Systems by Graphing or Substitution Solving Systems by Graphing or Substitution Objectives: Solve a system of linear equations in two variables by graphing

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Activity With your partner: Partner 1 - graph the equation 2x + 3y = 12 Partner 2 - assist partner 1 Partner 2 - graph the equation x – 4y = -5 Partner 1 - assist partner 2 How many points of intersection are there?1

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Activity With your partner: Partner 1 - graph the equation x = 2y + 1 Partner 2 - assist partner 1 Partner 2 - graph the equation 3x – 6y = 9 Partner 1 - assist partner 2 How many points of intersection are there?0

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Activity With your partner: Partner 1 - graph the equation 2x = 4 - y Partner 2 - assist partner 1 Partner 2 - graph the equation 6x + 3y = 12 Partner 1 - assist partner 2 How many points of intersection are there? an infinite number

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Classifying Systems of Equations consistent: at least one solution independent: exactly one solution dependent: infinite number of solutions inconsistent: no solution

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Example (1,1) Graph and classify each system. Then find the solution from the graph. consistent,independent

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Example 2 Graph and classify each system. Then find the solution from the graph. lets examine this graph with our calculators inconsistent no solution

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Practice Solve by graphing. 1)x + 4y = -6 2x – 3y = -1 2)y + 2x = 5 2y – 5x = 10 3)y – 2x = 7 y = 2x + 8 4)3y – 2x = 6 4x – 6y = -12

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Homework p.161 #11-23 odds USE GRAPH PAPER

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Warm-Up 6 minutes Graph and classify the system. Then find the solution from the graph.

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3.1.2 Solving Systems by Graphing or Substitution Solving Systems by Graphing or Substitution Objectives: Solve a system of linear equations by substitution

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Example 1 Solve using substitution. y = 3x 2x + 4y = 28 2x + 4(3x) = 28 2x + 12x = 28 14x = 28 x = 2 y = 3(2) y = 6 (2,6) y = 3x

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Example 2 Solve using substitution. 7x + y = 6 -7x y = -7x + 6 5x – (-7x + 6)= -3 5x + 7x – 6 = -3 12x – 6 = -3 12x = 3 7x + y = y = 6

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Example 3 Solve using substitution. 6z = -24 z = -4 x – y + 4 = -4 x + 8 x – y = -8 y = x + 8 5x + 2x = 7 7x + 28 = 7 5x + 2( )– 3( ) = 7-4 7x = -21 x = -3

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Practice Solve using substitution.

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Homework p.161 #27,29,31,39,41,45

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