1 / 28

i-can

Write down this problem on your READY RECALL SHEET Be prepared to explain your answer if you are called on.

tova
Download Presentation

i-can

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Write down this problem on your READY RECALL SHEET Be prepared to explain your answer if you are called on. Tate and Anna are selling pies for a school fundraiser. Customers can buy apple pies and blackberry pies. Tate sold 7 apple pies and 8 blackberry pies for a total of $155. Anna sold 2 apple pies and 4 blackberry pies for a total of $70. Write a system of equations to represent this situation (do not need to solve). i-can prepare for my Unit 11 Test by making a 3x5 card and completing my Practice Test.

  2. ITEMS of BUSINESS Test is on Monday/Tuesday. Also, it’s the last Day to turn in any absent/missing work. SAGE test is May 7-12. BE HERE.

  3. Questions on Homework? then Trade-n-Grade

  4. SYSTEMS OF EQUATIONS Unit 11 Review

  5. UNIT 11REVIEW CONCEPTS Remember It’s worth An extra 1% on your test! Write them down on your 3x5 card.

  6. POSSIBLE SOLUTIONS FOR 2 EQUATIONS (1,3) Infinitely Many Solutions One Solution No Solution Parallel Lines Same slope, different y-int. Coincidental Lines Same line, same slope, same y-int. Intersecting Lines Different Slope, y-int. can be different or the same Solve Algebraically: Variables drop out TRUE Statement ex. 22 = 22 Solve Algebraically: Variables drop out FALSE Statement ex. 12 = 9 Solve Algebraically: You will get one solution (X,Y)

  7. LETS TRY A FEW PROBLEMS Given the following systems, can You determine how many solutions (One, None, or Infinite) w/o graphing? B. y = - x + 5 y = x - 2 A. y = - x - 2 y = - x + 10 C. y = 9x - 1 y = -1 + 9x None Infinite One

  8. HOW MANY SOLUTIONS?

  9. SOLVE BY GRAPHING { y = - x + 3 y = 2x – 4 Solution: (3, 2)

  10. SOLVING BY GRAPHING { { y = - x + 5 y = - x y = 3x – 1 -3x + y = – 1 y = 3x -1 Infinite Solutions No Solution

  11. SOLVING BY SUBSTITUTION { x + y = 12 x = 2 + y It is of equal value. x is equal to 2 + y 2 + y can replace x 2 + y 2 + y + y = 12 We can solve this!

  12. { -5x + 5y = -5 x = -y + 5 A. Solve by Substitution: -5(-y + 5) + 5y = -5 Solution: (3, 2) 5y – 25 + 5y = -5 x, y 10y – 25 = -5 SUBSTITUTION +25 +25 x = -y + 5 10y = 20 x = -(2) + 5 x = -2 + 5 10 10 x = 3 y = 2 -5(3) + 5(2) = -5 3 = -2 + 5 Check: Are thesestatements TRUE?

  13. { 2x – 4y = 1 x = 2y + 3 B. Solve by Substitution: 2(2y + 3) – 4y = 1 4y + 6 – 4y = 1 SUBSTITUTION + 6 = 1 0y 6 = 1 Is this true? NO NO SOLUTION

  14. { C. Solve by Substitution: 4x – 2y = -10 y = 2x + 5 4x – 2(2x + 5) = -10 4x – 4x – 10 = -10 SUBSTITUTION – 10 = -10 0x -10 = -10 Is this true? YES INFINITE SOLUTIONS

  15. MATHICAL MATT/MAGGIE ARE YOU MATHICAL NOW? Show your Partner WE ARE USING THE ELIMINATION METHOD!! x + y = 30 x – y = 6 ADD THE TWO EQUATIONS TOGETHER & SOLVE 18 + y = 30 REPLACE x WITH 18 IN ONE OF THE ORIGINAL EQUATIONS & SOLVE FOR Y y = 30 - 18 2x = 36 y = 12 2 2 x = 18 x = 18,y = 12 (18,12)

  16. { 5x + 2y = 12 A. Solve by Elimination: -5x + 4y = -66 + 6y = -54 6 6 y = -9 ELIMINATION 5x + 2y = 12 5x + 2(-9) = 12 5x - 18 = 12 +18 +18 5x = 30 Solution: (6, -9) x, y 5 5 x = 6

  17. I WISH B.

  18. LETS PRACTICE WITH OUR COMMUNICATORS Example: Multiply both sides with 3 x + 2y = 7 3x + 6y = 21 A. Multiply both sides with 2 3x - y = 4 6x - 2y = 8 B. Multiply both sides with -4 x - 4y = 2 -4x + 16y = -8 C. Oppositize both sides x - 3y = -5 -x + 3y = 5

  19. { C. Solve by Elimination: ()3 ()2 2x – 4y = 6 -3x + 6y = -9 6x – 12y = 18 ELIMINATION + -6x + 12y = -18 0 = 0 Is this true? Yes! Infinite Solutions

  20. Solve by Elimination: { ()3 3x – 5y = -6-9x + 15y = 13 9x – 15y = -18 ELIMINATION + -9x + 15y = 13 0 = -5 Is this true? No! NO SOLUTION

  21. What does it Look Like? ONE SOLUTION: (X,Y) ONE SOLUTION: (X,Y) FALSE STATEMENT FALSE STATEMENT TRUE STATEMENT TRUE STATEMENT

  22. WHICH METHOD SHOULD I USE? 2x – 4y = 10 x = -6y + 12 5x + 8y = 3 -5x – 7 y = -2 ELIM SUB 5 -3x + 4y = 1 15x + 3y = -2 y = 2x - 4 -5x +2 y = -2 ELIM SUB y = 3/4x -5 y = 5x - 8 y = 6/7x +3 y = ½ x - 12 GRAPH GRAPH y = mx + b y = mx + b

  23. STORY PROBLEM The cost of making apple pies includes the booth rental of $180 and $4 per pie. We are charging $10 per pie. Write two equations, one representing the Production Cost and the other representing the Income. Assign y (dependent variable) to the Production Cost/Income and x (independent variable) to the number of pies sold. What does the solution represent? Production Cost: Income from Sales: Y = 180 + 4x Y = 10x Solve the above system. y = 10x y = 10(30) Using Substitution: 10x = 180 + 4x y = 300 -4x -4x 6x = 180 10x 6 6 Break-Even Point x = 30 Solution:(30, $300) The graph of the equations is to the right. The point of intersection is called the Break-Even Point. At least ______ apple pies must be sold to make a profit. 31

  24. Unit 11 Review i-can prepare for my Unit 11 Test by making a 3x5 card and completing my Practice Test.

  25. Practice Test Do the CIRCLED PROBLEMS on the PRACTICE TEST. When you finish, you can work on the rest of the problems.

  26. 15 2 7 Answers 17 8 19C 20 Y = 10 X 4C Y = 5C (10,50) 11 CARS 12 3 22 4 FALSE, VARIABLES DROP OUT, NO SOLUTION 14

  27. What’s your score? 21 possible -1 = 95% -2 = 90% -3 = 86% -4 = 81% -5 = 76% -6= 71% -7= 67% -8= 62% -9 or more: F Now, rework the ones you missed AND finish the rest of the practice test.

  28. Write down today’s homework on your CALENDAR CARD. WHITE Worksheet UNIT 11 PRACTICE TEST  SHOW YOUR WORK

More Related