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Table of Contents

Table of Contents. Topic Page #. . 6.6A Absolute Value Less ThAND 73. 6.6B Absolute Value GreatOR Than 74. 6.7 Two Variable Inequalities 75. 7.1 Solve Systems By Graphing 76. 7.2 Solve Systems By Substitution 77. 7.3 Solve Systems By Combination 78.

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Table of Contents

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  1. Table of Contents Topic Page # ... 6.6A Absolute Value Less ThAND 73 6.6B Absolute Value GreatOR Than 74 6.7 Two Variable Inequalities 75 7.1 Solve Systems By Graphing 76 7.2 Solve Systems By Substitution 77 7.3 Solve Systems By Combination 78

  2. Solve Systems by Substitution: • Line up the x and y values in standard form • Make one variable opposite each other if needed • Add the equations • Solve for the variable • Plug answer into any equation to find the other variable • Write answer as ordered pair (x,y)

  3. Example 1: Rewrite the linear system so that the like terms are arranged in columns 3x – y = 23 3x – y = 23 y + 8x = 11 a. 8x + y = 11

  4. Example 1: Rewrite the linear system so that the like terms are arranged in columns 4x – y = 1 4x = y + 1 3y + 4x = 7 b. 4x + 3y = 7

  5. Example 1: Rewrite the linear system so that the like terms are arranged in columns 7x – y = 13 7x – y = 13 y = 14x - 3 c. -14x + y = -3

  6. Example 2: Use the linear combination method to solve the system. 2x + 3(3) = 11 2x + 3y = 11 -2x + 5y = 13 + 2x + 9 = 11 8y = 24 2x = 2 y = 3 x = 1 (1, 3) ans:_______________

  7. 6x – 4y = 14 -3x + 4y = 1 + -3(5) + 4y = 1 3x = 15 -15 + 4y = 1 x = 5 4y = 16 y = 4 (5, 4) ans:_______________

  8. 4x – 3y = 5 –2x + 3y = -7 + -2(-1) + 3y = -7 2 + 3y = -7 2x = -2 x = -1 3y = -9 y = -3 (-1, -3) ans:_______________

  9. Example 3: Use the linear combination method to solve the system. 3x + 4y = -6 3x + 4y = -6 2y = 3x +6 + -3x + 2y = 6 6y = 0 y = 0 3x + 4(0) = -6 3x = -6 x = -2 (-2, 0) ans:_______________

  10. 8x – 4y = -4 8x – 4y = -4 4y = 3x + 14 + -3x + 4y = 14 5x = 10 x = 2 -3(2) + 4y = 14 -6 + 4y = 14 4y = 20 y = 5 (2, 5) ans:_______________

  11. 4x – 5y = –6 -5y = -4x – 6 2x + 5y = 12 + 2x + 5y = 12 6x = 6 x = 1 2(1) + 5y = 12 2 + 5y = 12 5y = 10 y = 2 (1, 2) ans:_______________

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