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Chapter 7 Systems of Linear Equations and Inequalities

Learn how to solve linear systems through graphing, substitution, linear combination, and inequalities graphing. Includes practice problems and special cases. Test on Tuesday 12/18.

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Chapter 7 Systems of Linear Equations and Inequalities

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  1. Chapter 7Systems of Linear Equations and Inequalities 7.1 Thursday 12/6 7.2 Friday12/7-Monday12/10 7.3 Tuesday12/11-Wed12/12 7.6 Thursday12/13-Friday12/14 Review Monday 12/17 Test Tuesday12/18

  2. 7.1 Solving Linear Systems by Graphing Objective -Solve a system of linear equations by graphing. Standards -A.1.2.2, A1.4.1, A1.5.1

  3. Terms • linear system • Solution of a system

  4. Rules • Get both equations in y=form • Graph both equations on the same graph paper • Find the point where the two lines cross • Write that point as an ordered pair • Special cases • If the lines are parallel there will be no solution • if the graph is of the same line there will be infinite solutions.

  5. Practice • Y = -x + 3 • Y = x + 1

  6. Practice • Y = 2x - 4 • Y = -½ x + 1

  7. Practice • -x + 2y = 6 • x + 4y = 24

  8. Practice • 2x – y = -2 • 4x – y = -6

  9. 7.2 Solving Linear Systems by Substitution Objective -Solve a system of linear equations by substitution. Standards -A.1.2.2, A1.5.3, A1.5.6

  10. Terms • Substitution • Transitive property

  11. Steps • Get both equations in y = form • Use the transitive property to make one new equation • Solve for x • Plug x into one of the original equations • Solve for y • Put you answer in ordered pair form

  12. Practice • y = x – 4 • y = -4x + 26

  13. Practice • y = 5 • y = -5x + 10

  14. Practice • y = 3x • x = 3y

  15. Practice • x – y = 2 • 2x + y = 1

  16. 7.3 Solving Linear Systems by Linear Combination Objective -Solve a system of linear equations by linear combination. Standards -A.1.5.4, A1.5.5, A1.5.6

  17. 7.6 Solving Systems of Linear Inequalities Objective -Solve a system of linear inequalities by graphing. Standards -A.1.4.6, A1.5.2, A1.5.6

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