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.
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ITEMS of BUSINESS Test is on Monday/Tuesday. Also, its the last
Day to turn in any absent/missing work. SAGE test is May 7-12. BE
HERE.
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Questions on Homework? then Trade-n-Grade
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SYSTEMS OF EQUATIONS Unit 11 Review
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Write them down on your 3x5 card. UNIT 11 REVIEW CONCEPTS
Remember Its worth An extra 1% on your test!
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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
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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 = -1 + 9x Infinite One None
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HOW MANY SOLUTIONS?
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SOLVE BY GRAPHING { Solution: (3, 2)
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SOLVING BY GRAPHING y = 3x 1 -3x + y = 1 { { No Solution
Infinite Solutions y = 3x -1
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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!
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A. Solve by Substitution: -5x + 5y = -5 x = -y + 5 { -5(-y + 5)
+ 5y = -5 5y 25+ 5y 10y 25 = -5 +25 10y = 20 10 y = 2 = -5 x = -y +
5 x = -(2) + 5 x = 3 Solution: (3, 2) x, y x = -2 + 5 SUBSTITUTION
-5(3) + 5(2) = -5 3 = -2 + 5 Check: Are these statements TRUE?
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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
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C. Solve by Substitution: 4x 2(2x + 5) = -10 4x 2y = -10 y = 2x
+ 5 { 4x 4x 10 0x 10 = -10 -10 = -10 Is this true? = -10 YES
SUBSTITUTION INFINITE SOLUTIONS
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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 = 30 - 18 y = 12 x = 18, y = 12
(18,12) MATHICAL MATT/MAGGIE WE ARE USING THE ELIMINATION
METHOD!!
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
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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
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Solve by Elimination: 15y { 3x 5y = -6 -9x + 15y = 13 9x -9x +
15y = 13 + 0 = -5 Is this true? ( ) 3 = -18 No! ELIMINATION NO
SOLUTION
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What does it Look Like? ONE SOLUTION: (X,Y) FALSE STATEMENT
TRUE STATEMENT
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WHICH METHOD SHOULD I USE? 5x + 8y = 3 -5x 7 y = -2 y = 2x - 4
-5x +2 y = -2 y = 3/4x -5 y = 5x - 8 2x 4y = 10 x = -6y + 12 -3x +
4y = 1 15x + 3y = -2 y = 6/7x +3 y = x - 12 SUB ELIM GRAPH 5 y = mx
+ b
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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 = 180 + 4x Y = 10x Using Substitution: 10x 10x = 180 + 4x
-4x 6x = 180 6 x = 30 y = 10x y = 10(30) y = 300 Solution: (30,
$300) Break-Even Point 31
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prepare for my Unit 11 Test by making a 3x5 card and completing
my Practice Test. Unit 11 Review
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Do the CIRCLED PROBLEMS on the PRACTICE TEST. When you finish,
you can work on the rest of the problems. Practice Test
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Answers 2 3 4 7 8 12 14 15 17 19C 20 22 Y = 10 X 4C Y = 5C
(10,50) 11 CARS FALSE, VARIABLES DROP OUT, NO SOLUTION
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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 Whats your score?
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SHOW YOUR WORK Write down todays homework on your CALENDAR
CARD. WHITE Worksheet UNIT 11 PRACTICE TEST