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DO NOW. How did you think you did on the last test? What parts of the test, did you think, you were successful in? What parts of the test, did you think, you were not successful in? What can you do to improve for the next test? What can I do to help improve your needs?. DO NOW. Turn it in.

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  1. DO NOW How did you think you did on the last test? What parts of the test, did you think, you were successful in? What parts of the test, did you think, you were not successful in? What can you do to improve for the next test? What can I do to help improve your needs? 2-1: Solving Linear Equations

  2. DO NOW Turn it in. 2-1: Solving Linear Equations

  3. Grade Distribution 2-1: Solving Linear Equations

  4. Solving Linear Equations by Graphing S E C T I O N 4 . 1 4.1: Solving Linear Equations by Graphing

  5. Definitions • Systems of Linear Equations • Requires 2 variables into two linear standard form equations • Solutions are systems of ordered pairs (x, y) 3-1: Solving Linear Equations through Graphing and Tables

  6. Example 1 Is (1, 3) a solution to the system, Plug the coordinates into the system. YES 3-1: Solving Linear Equations through Graphing and Tables

  7. Example 2 Is (1, –3) a solution to the system, Plug the coordinates into the system. NO 3-1: Solving Linear Equations through Graphing and Tables

  8. Your Turn Is (3, –2) a solution to the system, NO 3-1: Solving Linear Equations through Graphing and Tables

  9. Steps in Graphing Solutions • Put the equations into slope-intercept form and graph • Label answer in an ordered pair • Looking at the solution, classify the solution as: • Consistent System: A system that has at least ONE solution • Inconsistent System: A system that has NO solution • Independent System: A system that has EXACTLY one solution • Dependent System: A system that has INFINITE amount of solutions 3-1: Solving Linear Equations through Graphing and Tables

  10. Definitions 3-1: Solving Linear Equations through Graphing and Tables

  11. Definitions It does not have a solution set. Does it have at least one solution? It has more than one intersection point. (INFINITE) It has only one intersection point. 3-1: Solving Linear Equations through Graphing and Tables

  12. Example 3 Graph these equations, determine and classify the intersection points for this system Start out with the first equation and put it in y= form 3-1: Solving Linear Equations through Graphing and Tables

  13. Example 3 Graph these equations, determine and classify the intersection points for this system Find out the second equation and put it in y= form 3-1: Solving Linear Equations through Graphing and Tables

  14. Example 3 Graph these equations (4, 4) 3-1: Solving Linear Equations through Graphing and Tables

  15. Example 3 Classify the Solution Set (4, 4) Is the solution, Consistent or Inconsistent? If consistent, is it Independent or Dependent? 3-1: Solving Linear Equations through Graphing and Tables

  16. Example 3 Check to see if (4, 4) is the accurate solution to the system… 3-1: Solving Linear Equations through Graphing and Tables

  17. Example 4 Graph these equations, determine and classify the intersection points for this system Start out with the first equation and put it in y= form 3-1: Solving Linear Equations through Graphing and Tables

  18. Example 4 Graph these equations, determine and classify the intersection points for this system Find out the second equation and put it in y= form 3-1: Solving Linear Equations through Graphing and Tables

  19. Example 4 Graph these equations (1, 3) 3-1: Solving Linear Equations through Graphing and Tables

  20. Example 4 Classify the Solution Set (1, 3) Is the solution, Consistent or Inconsistent? If consistent, is it Independent or Dependent? 3-1: Solving Linear Equations through Graphing and Tables

  21. Example 4 Check to see if (1, 3) is the accurate solution to the system… 3-1: Solving Linear Equations through Graphing and Tables

  22. Your Turn Graph these equations, determine and classify the intersection points for this system (3, –1) 3-1: Solving Linear Equations through Graphing and Tables

  23. Using Graphing Calculator Graph these equations and determine the intersection points for this system 2nd TRACE 5 ENTER ENTER ENTER 3-1: Solving Linear Equations through Graphing and Tables

  24. y = x– 3 y = x– 3 Example 5 Graph these equations, determine and classify the intersection points for this system Start out with putting both equations into slope-intercept form 3-1: Solving Linear Equations through Graphing and Tables

  25. Example 5 Graph these equations, determine and classify the intersection points for this system 3-1: Solving Linear Equations through Graphing and Tables

  26. y = –4x + 1 y = –4x – 1 Example 6 Graph these equations, determine and classify the intersection points for this system Start out with putting both equations into slope-intercept form 4x + y = 1 y + 1 = –4x 3-1: Solving Linear Equations through Graphing and Tables

  27. Example 6 Graph these equations and determine the intersection points for this system 4x + y = 1 y + 1 = –4x 3-1: Solving Linear Equations through Graphing and Tables

  28. Assignment Page 240 1-5 odd, 9-21 EOO, 19 For 9-21 EOO and 19, label if it is consistent, inconsistent, dependent, and independent 4.1: Solving Linear Equations by Graphing

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