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Warm Up

Warm Up. Graph. 3x – 2y = 10. November 30, 2010. 7-1 Graphing Systems of Equations. Objective: Determine whether a system of linear equations has 0, 1, or infinitely many solutions. Solve systems of equations by graphing.

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Warm Up

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  1. Warm Up Graph. 3x – 2y = 10

  2. November 30, 2010 7-1 Graphing Systems of Equations Objective: Determine whether a system of linear equations has 0, 1, or infinitely many solutions. Solve systems of equations by graphing.

  3. Two equations together are called a system of equations.Example: 2x + y = 4 x + y = -1

  4. Three Cases: 1. Intersecting Lines Consistent and independent – have exactly one solution

  5. 2. Same Line Consistent and dependent – infinitely many solutions

  6. 3. Parallel Lines Inconsistent – no solution

  7. Systems of Equations(Tune: The wheels on the bus) Consistent, independent crosses one time, crosses one time, crosses one time Consistent, independent crosses one time IT HAS ONE SOLUTION! Consistent, dependent coincide, coincide, coincide, Consistent, dependent coincide IT HAS MANY SOLUTIONS! Inconsistent lines are parallel Parallel Parallel Inconsistent lines are parallel IT HAS ONE SOLUTION!

  8. Examples: Use the graph to determine how many solutions each system has. 1.

  9. 2.

  10. 3.

  11. One method of solving systems of equations is to carefully graph the equations on the same coordinate plane.

  12. Fill in Graphic Organizer Steps for Solving by GRAPHING: • Graph each line on the same coordinate plane. Graph by any of the following methods: • Put each in y = mx + b • X and Y intercepts • Table • The answer is the point where the two lines intersect.

  13. Examples: Graph, tell how many solutions the system has and if it has one solution, find it. 1. 2x – y = -3 8x – 4y = -12

  14. 2. x + 2y = 4 2x + y = 5

  15. x – 2y = 4 • x – 2y = -2

  16. 4. 2x + y = 10

  17. 5. x + y = 2 y = 4x + 7

  18. 6. x – 2y = 2 3x + y = 6

  19. 2x + 4y = 2 • 3x + 6y = 3

  20. 8. 3y = 2x

  21. Steps to solve systems of equations on TI-83 +:1. Solve for y.2. Put equations into y =3. 2nd Calc 5, Enter, Enter, Enter

  22. Class work Workbook p:

  23. Warm Up Solve by graphing. x + 2y = 0 3x + 4y = 4

  24. October 19, 2009 7-2 Substitution Objective: Solve systems of equations by using substitution.

  25. The exact solution of a system of equations can be found by using algebraic methods.

  26. SubstitutionTo solve a system of equations using substitution:1. Solve one of the equations for x or y to isolate one variable. (pick the easiest)2. Substitution the expression for x or y into the other equation.3. Solve for both x and y using algebra.

  27. Examples: Solve the system of equations. Check your answer. 1. x + 4y = 1 2x – 3y = -9

  28. 2. y = 3x – 8 y = 4 – x

  29. 3. 2x + 7y = 3 x = 1 – 4y

  30. 4. 4c = 3d + 3 c = d – 1

  31. 5. x + 3y = 12 x – y = 8

  32. 6. 2x + 3y = 1 -3x + y = 15

  33. 7. x + y = 0 3x + y = -8

  34. 8. 3x – 5y = 15

  35. 9. x + y = 4 2x + 2y = 8

  36. 10. 5x – y = 5 -4x + 5y = 17

  37. Classwork – Workbook Homework - Workbook

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