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Published byLeah Poole Modified over 6 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**

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?

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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 Graph and classify each system. Then find the solution from the graph. -8 -6 -4 -2 2 4 6 8 (1,1) consistent, independent

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**Example 2 inconsistent no solution**

Graph and classify each system. Then find the solution from the graph. inconsistent no solution let’s examine this graph with our calculators

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**Practice Solve by graphing. x + 4y = -6 2x – 3y = -1 y + 2x = 5**

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

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6 minutes Warm-Up 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**

Objectives: Solve a system of linear equations by substitution

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

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**Example 2 Solve using substitution. 7x + y = 6 -7x -7x y = -7x + 6**

= -3 7x + y = 6 5x + 7x – 6 = -3 7 + y = 6 12x – 6 = -3 12x = 3

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**Example 3 Solve using substitution. x – y + 4 = -4 x – y = -8**

– 3( ) -4 = 7 6z = -24 z = -4 5x + 2x = 7 7x + 28 = 7 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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