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.

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.

Questions on Homework?then Trade-n-Grade

SYSTEMS OF EQUATIONS

Unit 11 Review

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UNIT 11 REVIEW CONCEPTS

Remember It’s worth

An extra 1% on your test!

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

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

HOW MANY SOLUTIONS?

SOLVE BY GRAPHING

y = - x + 3y = 2x – 4 {

Solution: (3, 2)

SOLVING BY GRAPHINGy = - x + 5 y = - x

y = 3x – 1 -3x + y = – 1{{

No Solution Infinite Solutions

y = 3x -1

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!

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?

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

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

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!!

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

I WISH

𝐴 .3 𝑥+3 𝑦=−213 𝑥−2 𝑦=14

B.  

C .−4 𝑥+9 𝑦=9𝑥−3 𝑦=−6

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

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

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

What does it Look Like?

ONE SOLUTION: (X,Y) ONE SOLUTION: (X,Y)

FALSE STATEMENT FALSE STATEMENT

TRUE STATEMENT TRUE STATEMENT

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

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

i-can 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

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

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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UNIT 11PRACTICE

TEST