Homework check day! - PowerPoint PPT Presentation

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  1. Homework check day! • Please take out your homework from yesterday Academic: Rearranging equations sheet #1 – 3 Applied: Page 3 #4, 6, 10

  2. Solving Linear Systems Graphically Friday, Jan 31st

  3. Review: Solving Equations A single equation with one variable has just one solution. Example: –2 – 5x = 13 • x = 2 • x = -2 • x = 3 • x = -3

  4. Review: Solving Equations A single equation with one variable has just one solution. Example: –2 – 5x = 13 • x = 2 • x = -2 • x = 3 • x = -3

  5. Review: Solving Equations A single equation with two variables has infinite solutions. Which of the following is a solution to: 3x – 2y = 5 • (1, -4) • (1, 4) • (-1, 4) • (-1, -4)

  6. Review: Solving Equations A single equation with two variables has infinite solutions. Which of the following is a solution to: 3x – 2y = 5 • (1, -4) • (1, 4) • (-1, 4) • (-1, -4)

  7. Review: Solving Equations A system of two equations with two common variables has justone solution. Example: x – y = 4 x + 2y = 13 A) x = 6, y = 2 B) x = 5, y = 4 C) x = 7, y = 3 D) x = 8, y = 4

  8. Review: Solving Equations A system of two equations with two common variables has justone solution. Example: x – y = 4 x + 2y = 13 A) x = 6, y = 2 B) x = 5, y = 4 C) x = 7, y = 3 D) x = 8, y = 4

  9. Solving Equations with Fractions Example: 3 4 A B = Solution: 4 3 A = B

  10. Solving Equations with Fractions Example: 7 2 B = – A Solution: 2 7 A = – B

  11. Try it! You have 2 minutes to try the last two questions on your sheet from yesterday!

  12. Review: Graphing Linear Functions What is the slope of y = 3x + 1 • 3 • 1 • 1/3 • -1/3

  13. Review: Graphing Linear Functions What is the slope of y = 3x + 1 • 3 • 1 • 1/3 • -1/3

  14. Review: Graphing Linear Functions What is the x-intercept of y = 3x + 1 • 3 • 1 • 1/3 • -1/3

  15. Review: Graphing Linear Functions What is the x-intercept of y = 3x + 1 • 3 • 1 • 1/3 • -1/3

  16. Review: Graphing Linear Functions What is the y-intercept of y = 3x + 1 • 3 • 1 • 1/3 • -1/3

  17. Review: Graphing Linear Functions What is the y-intercept of y = 3x + 1 • 3 • 1 • 1/3 • -1/3

  18. Review: Graphing Linear Functions Graph y = 3x + 1

  19. Review: Graphing Linear Functions In your teams, sketch a graph of the following on a whiteboard: y = 2x – 3 y = ½x + 1 y = –2x + 3 Extra challenge: Graph 6x – 2y = 8

  20. Review: Graphing Linear Functions In your teams, sketch a graph of the following on a whiteboard: y = 2x – 3 y = ½x + 1 y = –2x + 3 Extra challenge: Graph 6x – 2y = 8

  21. New Methods for Solving Equation Systems! Today’s method for solving equations: graph them!

  22. Solving Equations Graphically Example: In the Barcelona Olympics, Canadian men and women won a total of 7 gold medals. Women athletes won one more gold medal than the men athletes. • Set up equations to describe this scenario x + y = 7 y – x = 1 X = number of male medalists Y = number of female medalists

  23. Solving Equations Graphically Example: In the Barcelona Olympics, Canadian men and women won a total of 7 gold medals. Women athletes won one more gold medal than the men athletes. • Set up equations to describe this scenario x + y = 7 y – x = 1 X = number of male medalists Y = number of female medalists • Rearrange each equation for y y = –x + 7 y = x + 1

  24. Solving Equations Graphically • Rearrange each equation for y y = –x + 7 y = x + 1 • Graph each equation and look for their intersection point (3, 4)

  25. Solving Equations Graphically In teams of two, use the graphing calculator on the ipads to solve the following systems of equations: • y = –3x + 7, y = 4x – 5 • 10x + 2y = 8, 3y – x = 12 • x – 3y = 27, 2y + x = 20 Next, attempt to solve the following systems of equations: • y = 2x + 3, y = 2x – 1 • y = –x + 3, 2x + 2y = 6 What do you notice about the solutions to #4 and #5?

  26. Solving Equations Graphically There are three kinds of linear equations: • Intersecting – has one solution Different slopes 2) Parallel – has no solutions Same slope, different intercepts 3) Coincident – has infinite solutions Same slope, same intercepts

  27. Individual Practice Using the ipads, try problems: Page 12 #1, 3, 5 – 8 (do a,c,e,…) Homework: Page 4 - 5 1-ordered pairs and one equation #1, 2 2-ordered pairs and two equations #1, 2 3-problem solving #1 Rearranging equations sheet #4, 5