i-can
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Transcript of i-can
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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
Write down this problem on yourREADY RECALL SHEET
Be prepared to explain your answer if you are called on.
prepare for my Unit 11 Test bymaking a 3x5 card and completing myPractice Test.
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ITEMS of BUSINESS
Test is on Monday/Tuesday. Also, it’s the lastDay 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 It’s worth
An extra 1% on your test!
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POSSIBLE SOLUTIONS FOR 2 EQUATIONS
One Solution No SolutionInfinitely
Many Solutions
(1,3)
Intersecting LinesDifferent Slope, y-int. can be
different or the same
Solve Algebraically: You will get one solution
(X,Y)
Parallel LinesSame slope, different y-int.
Solve Algebraically: Variables drop out FALSE Statement
ex. 12 = 9
Coincidental LinesSame 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?A. y = - x - 2 y = - x + 10
B. y = - x + 5 y = x - 2
C. y = 9x - 1 y = -1 + 9x
InfiniteOneNone
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HOW MANY SOLUTIONS?
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SOLVE BY GRAPHING
y = - x + 3y = 2x – 4 {
Solution: (3, 2)
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SOLVING BY GRAPHINGy = - x + 5 y = - x
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 + yx is equal to 2 + y
{2 + y can replace xIt 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 +25
10y = 20 10 10
y = 2
= -5
x = -y + 5x = -(2) + 5
x = 3
Solution: (3, 2) x, y
x = -2 + 5
SUBS
TITU
TIO
N
-5(3) + 5(2) = -5
3 = -2 + 5Check: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
NOSU
BSTI
TUTI
ON
NO SOLUTION
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C. Solve by Substitution:
4x – 2(2x + 5) = -10
4x – 2y = -10y = 2x + 5 {
4x – 4x – 10 0x – 10 = -10
-10 = -10Is this true?
= -10
YESSUBS
TITU
TIO
N
INFINITE SOLUTIONS
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x + y = 30x – y = 6 ADD THE TWO
EQUATIONS TOGETHER & SOLVE
2x = 362 2x = 18
REPLACE x WITH 18IN ONE OF THE ORIGINAL
EQUATIONS & SOLVE FOR Y
18 + y = 30y = 30 - 18y = 12
x = 18, y = 12 (18,12)
MATHICAL MATT/MAGGIE
ARE YOUMATHICAL
NOW? Show your PartnerWE ARE USING THE ELIMINATION METHOD!!
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A. Solve by Elimination:{ 5x + 2y = 12
-5x + 4y = -66+ 6y = -54 6 6y = -9
5x + 2y = 12 5x + 2(-9) = 12
5x - 18 = 12+18 +18
5x = 305 5
x = 6
Solution: (6, -9)
x, y
ELIM
INAT
ION
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I WISH
𝐴 .3 𝑥+3 𝑦=−213 𝑥−2 𝑦=14
B.
C .−4 𝑥+9 𝑦=9𝑥−3 𝑦=−6
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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 = 8B. 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
ELIM
INAT
ION
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Solve by Elimination:
– 15y
{ 3x – 5y = -6 -9x + 15y = 13
9x-9x + 15y = 13+
0 = -5Is this true?
( ) 3
= -18
No!ELIM
INAT
ION
NO SOLUTION
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What does it Look Like?
ONE SOLUTION: (X,Y) ONE SOLUTION: (X,Y)
FALSE STATEMENT FALSE STATEMENT
TRUE 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 -5y = 5x - 8
2x – 4y = 10x = -6y + 12
-3x + 4y = 115x + 3y = -2
y = 6/7x +3y = ½ x - 12
SUB
SUB
ELIM
ELIM
GRAPH GRAPH
5
y = mx + b 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 + 4xY = 10x
Using Substitution:
10x
10x = 180 + 4x-4x -4x
6x = 180 6 6 x = 30
y = 10x y = 10(30) y = 300
Solution: (30,
$300)
Break-Even Point
31
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i-can 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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Answ
ers2
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
What’s your score?
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Write down today’s homework on yourCALENDAR CARD.
WHITEWorksheet
UNIT 11PRACTICE
TEST