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). Write down this problem on your READY RECALL SHEET Be prepared to explain your answer if you are called on. prepare for my Unit 11 Test by making a 3x5 card and completing my Practice Test.

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 BE HERE.

Questions on Homework? then Trade-n-Grade

SYSTEMS OF EQUATIONS Unit 11 Review

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

POSSIBLE SOLUTIONS FOR 2 EQUATIONS (1,3) Intersecting Lines Different Slope, y-int. can be different or the same Solve Algebraically: You will get one solution (X,Y) Parallel Lines Same slope, different y-int. Solve Algebraically: Variables drop out FALSE Statement ex. 12 = 9 Coincidental Lines Same line, same slope, same y-int. Solve Algebraically: Variables drop out TRUE Statement ex. 22 = 22

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

HOW MANY SOLUTIONS?

SOLVE BY GRAPHING { Solution: (3, 2)

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

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

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

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

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

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

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

I WISH

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

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

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

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

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

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. Production Cost: Income from Sales: Solve the above system. What does the solution represent? 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. Y = x Y = 10x Using Substitution: 10x 10x = x -4x 6x = x = 30 y = 10x y = 10(30) y = 300 Solution: (30, $300) Break-Even Point 31

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

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

Answers C Y = 10 X 4C Y = 5C (10,50) 11 CARS FALSE, VARIABLES DROP OUT, NO SOLUTION

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

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