1. Monday, 1/24Tuesday, 1/25Wednesday, 1/26Thursday, 1/27Friday, 1/28 Final corrections Systems of equations: graphing No classes – End of S1 Monday, 1/31Tuesday, 2/1Wednesday, 2/2Thursday, 2/3Friday, 2/4 Systems of equations: substitution EXPLORE Testing Work Keys Testing Report Card Pick-Up 4PM –6PM (EC) Systems of equations: Elimination using addition/ subtraction Systems of equations: elimination using multiplication Monday, 2/7Tuesday, 2/8Wednesday, 2/9Thursday, 2/10Friday, 2/11 Quiz: Systems of Equations Review for test Review for test Test: Systems of equations No classes – Staff Dev Day Valentines Dance: 7PM – 11PM

2. 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 (same line.) If the two equations have no points in common, the system of equations has no solution (parallel lines.)

3. 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. x – y = 2 + y +y x = 2 + y - 2 -2 x – 2 = y 3y + 2x = 9 - 2x -2x 3y = -2x + 9 333

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

5. 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.

6. x y 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).

7. The two equations in slope- intercept form are: x y 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.

8. x y 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.

9. 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

10. Activity-Systems of equations: Graphing Each pair has a note card with a system of equations Working in pairs: 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.) This will be our first project grade. 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

11. Mon, 1/31 SWBAT… solve systems of equations using the substitution method Agenda 1. WU (10 min) 2. Announcements (5 min) 3. Examples – Systems of equations: substitution method Warm-Up: 1. Describe the advantages and disadvantages to solving systems of equations by graphing. 2. Compare m and b (same or different) Number of Solutions One None Infinite

12. Monday, 1/24Tuesday, 1/25Wednesday, 1/26Thursday, 1/27Friday, 1/28 Final corrections Systems of equations: graphing No classes – End of S1 Monday, 1/31Tuesday, 2/1Wednesday, 2/2Thursday, 2/3Friday, 2/4 Systems of equations: substitution EXPLORE Testing (8:45-12) Adv 406: Rm 206 Adv 407: Rm 208 Adv 408: Rm 201 Adv 409: Mac Lab WorkKeys Testing (8:45-12) Report Card Pick-Up 4PM–6PM (EC) Systems of equations: Elimination using addition/ subtraction Systems of equations: elimination using multiplication Monday, 2/7Tuesday, 2/8Wednesday, 2/9Thursday, 2/10Friday, 2/11 Quiz: Systems of Equations Review for test Review for test Test: Systems of equations No classes – Staff Dev Day Valentines Dance: 7PM – 11PM Tuesday’s & Wednesday’s testing rooms

13. Announcements Welcome to Quarter 3, Semester 2!!! All students start this new semester with 100% (A+).  Your job is to keep it!! Everyone has been given 100 work ethic points. For the second semester:  Each tardy will result in a deduction of 10 points.  Not having your planner will result in a deduction of 10 points.  Not wearing your ID or Infinity polo will result in a deduction of 10 points each.  Wearing hats, hoodies, jackets, fleeces, or ear buds will result in a deduction of 10 points each, will be confiscated, and will not be returned until the end of the day. (These items apply in the hallways, cafeteria, advisories also – not just in class)

14. Mean: 86% Range: 60% - 99.9%

15. Conclusions Compare m and b Number of Solutions One None Infinite

16. Conclusions Compare m and b Number of Solutions Different m values (b can be same or different) One None Infinite

17. Conclusions Compare m and b Number of Solutions Different m values (b can be same or different) One Same m value, but different b values None Infinite

18. Conclusions Compare m and b Number of Solutions Different m values (b can be same or different) One Same m value, but different b values None Same m value and same b value Infinite

19. HW#1: Systems-Graphing Method Answers: 1. 1 Solution: (1, 2) 2. 1 Solution: (-4, -2) 3. Infinite Solutions 4. 1 Solution: (-2, -2) 5. 1 Solution: (-3, 5) 6. Infinite Solutions 7. Infinite Solutions 1. Top equation: multiply by 5/8 2. Bottom equation: multiply by 5/2 8. 1 Solution: (3, -3) 1. Top equation: multiply by 3/2 2. Bottom equation: multiply by 5/1

20. Systems of equations: substitution method Example 1: Solve the system using substitution The sum of two numbers is 20. The difference between three times the larger number and twice the smaller is 40. Follow the directions from the box and solve the above system. The steps to solving systems of equations using the substitution method are shown in the box on HW#2

21. How can you verify that your solution is correct? x + y = 20 3x – 2y = 40 Answer: (4, 16)

22. Example 2: Solve the system using substitution 3x = 3y + 3 x – y = 1

23. HW#2: Substitution Answers 1. (5, 10) 2. (0, 2) 3. (2, 0) 4. No Solution 5. Infinite Solution 6. (0, -6) 7. a.) t = cost of a taco, b = cost of a burrito 8. b.) 3t + 2b = 7.40 4t + 1b = 6.45 9. c.) c = 1.1, b = 2.05 10. d.) The cost of 2 tacos is $2.20 and the cost of 2 burritos is $4.10.

24. Thurs, 2/27 SWBAT… solve systems of equations using the elimination method Agenda 1. WU (10 min) 2. Review hw (10 min) 3. 3 Examples – Systems of equations: elimination method (15 min) WU: Use substitution to solve the system of equations 1.) y = 2x – 4 2.) x = y – 1 -6x + 3y = -12 -x + y = -1 HW#3: Elimination method

25. Ex.1: Elimination using Addition 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. -3x + 5y = -11 3x + 7y = -1

26. Ex. 2: Elimination using Subtraction 2t + 5r = 6 9r + 2t = 22

27. Mon, 1/31 SWBAT… solve systems of equations using elimination using multiplication Agenda 1. WU (10 min) 2. One example: elimination using multiplication (10 min) 3. Review hw#3: elimination (10 min) 4. Concept Summary – Solving Systems of Equations (15 min) WU: Solve using elimination using multiplication: 1. 5x + 6y = -8 2x + 3y = -5 2. Verify that your solution is correct. HW#4: Systems of Equations: Real-life and HW#5: Systems of Equations – MC

28. Announcements Welcome to Quarter 3, Semester 2!!! All students start this new semester with 100% (A+).  Your job is to keep it!! Everyone has been given 200 work ethic points. For the second semester:  Each tardy will result in a deduction of 25 points.

29. Mean: 86% Range: 57% - 99%

30. Elimination using Multiplication 9x + 5y = 34 8x – 2y = -2

31. HW#3: Elimination Answers 1. (5, 2) 2. (1, 6) 3. (6, 1) 4. (-3, 5) 5. (4, -1) 6. (2, 3) 7. (2, -3) 8. (1, 2) 9. x = 6, y = 18 10. c = 3.95, a = 5.95 11. a.) (4, 1) 12. d.) (0, 3) (2, 5)

32. Fill in the chart below: MethodThe Best Time to Use Graphing Substitution Elimination using Addition Elimination using Subtraction Elimination using Multiplication

33. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. Substitution Elimination using Addition Elimination using Subtraction Elimination using Multiplication

34. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. Substitution If one of the variables in either equation has a coefficient of 1 or -1. Elimination using Addition Elimination using Subtraction Elimination using Multiplication

35. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. Substitution If one of the variables in either equation has a coefficient of 1 or -1. Elimination using Addition If one of the variables has opposite coefficients in the two equations. Elimination using Subtraction Elimination using Multiplication

36. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. Substitution If one of the variables in either equation has a coefficient of 1 or -1. Elimination using Addition If one of the variables has opposite coefficients in the two equations. Elimination using Subtraction If one of the variables has the same coefficient in the two equations. Elimination using Multiplication

37. Fill in the chart below: MethodThe Best Time to Use Graphing To estimate solutions, since graphing usually does not give an exact solution. Substitution If one of the variables in either equation has a coefficient of 1 or -1. Elimination using Addition If one of the variables has opposite coefficients in the two equations. Elimination using Subtraction If one of the variables has the same coefficient in the two equations. Elimination using Multiplication If none of the coefficients are 1 or -1 and neither of the variables can be eliminated by simply adding or subtracting the equations.

38. Which method is best to use? Why? 1.x = 12y – 14 3y + 2x = -2 Substitution; one equation is solved for x 2. 20x + 3y = 20 -20x + 5y = 60 Elimination; add to eliminate x 3.y = x + 2 y = -2x + 3 Substitution; both equations are solved for y

39. HOMEWORK: HW#1 – HW#5 will be collected on Friday. Quiz on systems on Friday. Extra Credit: Find a value of n such that the x-value of the solution of the system below is 4. Show or explain your work. 5x – 10y = 50 nx + 10y = 6

40. 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?

41. 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?

42. 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?