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Tuesday, 2/9/10 SWBAT… solve systems of equations using the graphing method

Tuesday, 2/9/10 SWBAT… solve systems of equations using the graphing method. Agenda WU (5 min) Activity – Systems of equations: graphing method (20 min) Presentations (15 min) Conclusions (10 min) Warm-Up: Write hw in planner

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Tuesday, 2/9/10 SWBAT… solve systems of equations using the graphing method

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  1. Tuesday, 2/9/10SWBAT… solve systems of equations using the graphing method Agenda • WU (5 min) • Activity – Systems of equations: graphing method (20 min) • Presentations (15 min) • Conclusions (10 min) Warm-Up: • Write hw in planner • Read the graphing/ substitution/ elimination examples • Questions from back of agenda problems? HW#1: Graphing method

  2. Systems of Equations: Graphing Method • What are systems of equations? • A collection of equations involving the same set of variables. • We will be dealing with two equations and two variables.

  3. Activity-Systems of equations: Graphing • I have given one person a note card with a system of equations • You are to work with a person who has a note card • Directions: Graph the system of equations on a big piece of graph paper. Determine whether the system has one solution, no solution, or infinite solutions. If the system has one solution, name it (see worksheet on how to name it.) • Show your work on your graph paper (don’t write on the note card) • After 20 minutes, I will randomly choose 3 groups to present their system

  4. Conclusions • The solution to a systems of equations is the point where the two lines intersect (one solution) • No solution will be parallel lines • Infinite solution will be the same line

  5. Solving Systems of Equations by Graphing • Step 1) Write the equations of the lines in slope-intercept form. • Step 2) Graph each line on the same graph. • Step 3) Determine the point of intersection and write this point as an ordered pair. • If the two equations represent the same line, the system of equations has infinitely many solutions. • If the two equations have no points in common, the system of equations has no solution.

  6. Example Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution. x – y = 2 3y + 2x = 9 Step 1: Write each equation in slope-intercept form. 3y + 2x = 9 - 2x -2x x – y = 2 + y +y 3y = -2x + 9 x = 2 + y - 2 -2 3 3 3 x – 2 = y

  7. y x Step 2: Graph each line on the same graph Step 3: Determine the point of intersection. y = x – 2 The point of intersection of the two lines is the point (3,1). This system of equations has one solution, the point (3,1) .

  8. Additional Examples Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution.

  9. y x Problem 1 The two equations in slope-intercept form are: Plot points for each line. Draw in the lines. These two equations represent the same line. Therefore, this system of equations has infinitely many solutions .

  10. y x Problem 2 The two equations in slope-intercept form are: Plot points for each line. Draw in the lines. This system of equations represents two parallel lines. This system of equations has no solution because these two lines have no points in common.

  11. y x Problem 3 The two equations in slope-intercept form are: Plot points for each line. Draw in the lines. This system of equations represents two intersecting lines. The solution to this system of equations is a single point (3,0).

  12. Wed, 2/10/10SWBAT… solve systems of equations using the substitution method Agenda • WU (5 min) • Examples – Systems of equations: substitution method Warm-Up: • Write hw in planner • Describe the advantages and disadvantages to solving systems of equations by graphing. HW#2: Substitution method HW#3: Elimination method

  13. Conclusions

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  16. Conclusions

  17. Set up a systems of equations (substitution method) The sum of two number is 20. The difference between three times the larger number and twice the smaller is 40.

  18. Tues, 2/16/10SWBAT… solve systems of equations using the elimination method Agenda • WU (10 min) • 3 Examples – Systems of equations: elimination method (15 min) • Work on hw#1, 2, or 3 (20 min) • Turn in hw#1/2 WU: Use the substitution to solve the system of equations y = 2x – 4 x = y – 1 -6x + 3y = -12-x + y = -1 HW#3: Elimination method

  19. Elimination using Addition Use the elimination method to solve the system of equations: -3x + 5y = -11 3x + 7y = -1 Negative three times one number plus five times another number is -11. Three times the first number plus 7 times the other number is -1. Find the numbers.

  20. Elimination using Subtraction Use the elimination method to solve the system of equations: 2t + 5r = 6 9r + 2t = 22

  21. Elimination using Multiplication Use the elimination method to solve the system of equations: 5x + 6y = -8 2x + 3y = -5

  22. Wed, 2/17/10SWBAT… apply systems of equations Agenda • WU (5 min) • Concept Summary – Solving Systems of Equations (15 min) • Real-life systems examples Warm-Up: • Write hw in planner • Questions from hw #3-elimination? HW#4: Real-life systems of equations

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  29. How a customer uses systems of equations to see what he paid Two groups of students order burritos and tacos at Atontonilco. One order of 3 burritos and 4 tacos costs $11.33. The other order of 9 burritos and 5 tacos costs $23.56. How much did each taco and burrito cost?

  30. How a fair manager uses systems of equations to plan his inventory The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2,200 people enter the fair and $5,050 is collected. How many children and how many adults attended?

  31. How a manager uses systems of equations to plan employee time The local bakery is making chocolate chip cookies and bread. Each batch of cookies take 20 minutes to prepare and 10 minutes to bake. Each loaf of bread takes 10 minutes to prepare and 30 minutes to bake. The bakery’s management has allotted 800 minutes of employee time (preparation) and 900 minutes of oven time (baking). How many of each should be baked?

  32. How a customer uses systems of equations to see what he paid A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bills do not list the per-item price. What were the costs of one bush and of one tree?

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