1. Quiz Date 1/22/19 Change For version B #5 𝒚=𝟐𝒙+𝟔 𝒚=𝟓𝒙
Pick up your homework from the back table
Work on your quiz
No EQ and No Warm-up.
Change
For version B #5
𝒚=𝟐𝒙+𝟔 𝒚=𝟓𝒙
Essential Question: None
Yes you can used your notes
Warm Up: None
When done, turn in your quiz and any work to the BACK TABLE
Then, work on this week’s homework.

2. Tuesday 01/22/19 Homework solution
Solve the system of equation by any method 1.
𝑦=− 1 2 𝑥+2 𝑦=𝑥+8
Solve by graphing because the equations are in
slope intercept form of 𝑦=𝑚𝑥+𝑏
𝑦=− 1 2 𝑥+2 First equation
Slope = − y-intercept is 2
𝑦=𝑥+8 Second equation
Slope = y-intercept is 8
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏 ( −4, 4)

3. Tuesday 01/22/19 Homework solution
Solve the system of equation by any method 2.
𝑦−2𝑥=3 2𝑦−12=𝑥
Solve by Substation because the x is already solve for
Step 1: Determine the equation that is solve for
𝑥=2𝑦−12
Step 2: Substitute the solve equation into the other equation
𝑦−2 2𝑦−12 =3
Step 3: Simplify and solve for the variable
𝑦−4𝑦+24=3 Distribute
−3𝑦+24=3 Combine the variable
−3𝑦=−21 Subtract 24 to both sides
𝑦=7 Divide by -3 to both sides

4. WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 2,7)
Step 4: Substitute the solved variable back into the original to get the other variable 𝑦−2𝑥=3 First equation (7)−2𝑥=3 Substitute 𝑦=7 7−2𝑥=3 −2𝑥=−4 Subtract 7 to both sides 𝑥=2 Divide by -2 to both sides
The solution of a system is always in the format of an order pair
(7,2)
WRONG
An order pair is ( 𝑥, 𝑦)
Correct order pair ( 2,7)

5. Tuesday 01/22/19 Homework solution
Solve the system of equation by any method 3.
𝑦=2𝑥+3 𝑦= 1 2 𝑥+6
Solve by graphing because the equations are in
slope intercept form of 𝑦=𝑚𝑥+𝑏
𝑦=2𝑥+3 First equation
Slope = y-intercept is 3
𝑦= 1 2 𝑥+6 First equation
Slope = y-intercept is 6
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏 ( 2, 7)

6. 5.3 Solve System by Elimination Date 1/23/19
Copy down Essential Question.
Work on Warm Up.
Essential Question
How would you describe the process of solving for a system using Elimination?
Warm Up: Explain the different between the two things.
𝑥+3𝑦=−2 𝑥=3𝑦+16
𝑥+3𝑦=−2 𝑥−3𝑦=16
Solve by substitution
DON’T Solve by substitution

7. Understand when to solve by Elimination
𝑥+3𝑦=−2 𝑥=3𝑦+16
𝑥+3𝑦=−2 𝑥−3𝑦=16
Solve by substitution
DON’T Solve by substitution
𝒙 is already solve for
notice 𝑥=3𝑦+16
nothing is solve for
For this we use
Elimination

8. How to solve by Elimination
𝑥+3𝑦=−2 𝑥−3𝑦=16 Step 1: check that the coefficient of the one of the variable are opposites. 𝑥+3𝑦=−2 𝑥−3𝑦=16 The coefficient of the y are opposites Step 2: Add the two equations(one variable should disappear) .
One equation with one unknown

9. Step 3: Solve for the variable you have left Step 4: Substitute the solved variable back into one of the original equation to solve for other variable. The solution needs to be in a order pair.

10. Checking your answer The solution is (7, −3)
Equation 1 𝑥+3𝑦=−2 (7)+3(−3)=−2 −2=−2 Equation 2 𝑥−3𝑦=16 7 −3(−3)=16 16=16

11. Wednesday 01/23/19 Homework solution
Solve the system of equation by elimination 1.
3𝑦+2𝑥=6 5𝑦−2𝑥=10
Solve by elimination because the coefficient of x are opposite
Step 1: check that the coefficient of the one of the variable are opposites.
3𝑦+2𝑥=6 5𝑦−2𝑥=10
Step 2: Add the two equations together (one variable should disappear)
3𝑦+2𝑥=6 5𝑦−2𝑥=10 8𝑦 =16
Step 3: Simplify and solve for the variable
8𝑦=16
𝑦=2 Divide by 8 to both sides

12. WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 0, 2)
Step 4: Substitute the solved variable back into the original to get the other variable 3𝑦+2𝑥=6 First equation 3(2)−2𝑥=6 Substitute 𝑦=2 6−2𝑥=6 −2𝑥=0 Subtract 6 to both sides 𝑥=0 Divide by -2 to both sides
The solution of a system is always in the format of an order pair
(2,0)
WRONG
An order pair is ( 𝑥, 𝑦)
Correct order pair ( 0, 2)

13. Wednesday 01/23/19 Homework solution
Solve the system of equation by elimination 2.
5𝑦+4𝑥=22 −12𝑦−4𝑥=−36
Solve by elimination because the coefficient of x are opposite
Step 1: check that the coefficient of the one of the variable are opposites.
5𝑦+4𝑥=22 −12𝑦−4𝑥=−36
Step 2: Add the two equations together (one variable should disappear)
5𝑦 𝑥 = 22 −12𝑦−4𝑥 =−36 −7𝑦 =−14
Step 3: Simplify and solve for the variable
−7𝑦=−14
𝑦=2 Divide by -7 to both sides

14. WRONG An order pair is ( 𝑥, 𝑦) Correct order pair ( 3, 2)
Step 4: Substitute the solved variable back into the original to get the other variable 5𝑦+4𝑥=22 First equation 𝑥=22 Substitute 𝑦=2 10+4𝑥=22 4𝑥=12 Subtract 10 to both sides 𝑥=3 Divide by 4 to both sides
The solution of a system is always in the format of an order pair
(2,3)
WRONG
An order pair is ( 𝑥, 𝑦)
Correct order pair ( 3, 2)

15. Wednesday 01/23/19 Homework solution
Solve the system of equation by elimination 3.
3𝑥−𝑦=5 𝑥+𝑦=3
Solve by elimination because the coefficient of y are opposite
Step 1: check that the coefficient of the one of the variable are opposites.
3𝑥−𝑦=5 𝑥+𝑦=3
Step 2: Add the two equations together (one variable should disappear)
3𝑥 − 𝑦 = 5 𝑥 + 𝑦 = 3 4𝑥 =8
Step 3: Simplify and solve for the variable
4𝑥=8
𝑥=2 Divide by 4 to both sides

16. Correct order pair ( 2, 1) An order pair is ( 𝑥, 𝑦)
Step 4: Substitute the solved variable back into the original to get the other variable 𝑥+𝑦=3 second equation (2)+𝑦=3 Substitute x=2 2+𝑦=3 y=1 Subtract 2 to both sides
The solution of a system is always in the format of an order pair
Correct order pair ( 2, 1)
An order pair is ( 𝑥, 𝑦)

17. 5.3 Solve System by Elimination Day 2 Date 1/24/19
Copy down Essential Question.
Work on Warm Up.
Fix error on homework
Essential Question
How is solving a system using elimination different that solving using substitution?
Warm Up: Add the two equation in each problem.
𝑥−2𝑦 = −19 5𝑥+2𝑦 = 𝑥+4𝑦 =18 −2𝑥+4𝑦 = 8
6𝑥 =−18 𝑥+8𝑦=26

18. Describe the process of solving a system by Elimination in your own words
3𝑥+2𝑦=4 3𝑥−2𝑦=−4
Step 1:
Step 2:

19. Step 3:
Step 4:
The solution needs to be in a order pair.

20. Practice on solving by Elimination
2𝑥−𝑦=9 4𝑥+𝑦=21 Step 1: check that the coefficient of the one of the variable are opposites. 2𝑥−1𝑦=9 4𝑥+1𝑦=21 The coefficient of the y are opposites Step 2: Add the two equations(one variable should disappear) .

21. Step 3: Solve for the variable you have left Step 4: Substitute the solved variable back into one of the original equation to solve for other variable. The solution needs to be in a order pair.
The solution is (5, 1)

22. How to solve by Elimination when there is the same number but they are not opposite
3𝑥+4𝑦=18 −2𝑥+4𝑦=8

23. How to solve by Elimination when there is the same number but they are not opposite
Step 1: check that the coefficient of the one of the variable are opposites. 3𝑥+4𝑦=18 −2𝑥+4𝑦=8 Step 1b: 3𝑥+4𝑦=18 −1(−2𝑥+4𝑦=8) Result 3𝑥+4𝑦=18 2𝑥−4𝑦=−8

24. 3𝑥+ 4𝑦 = 18 2𝑥 −4𝑦 =−8 5𝑥 =10 (2, 3) Solution An order pair is ( 𝑥, 𝑦)
Step 2: Add the two equations together (one variable should disappear)
3𝑥+ 4𝑦 = 𝑥 −4𝑦 =−8 5𝑥 =10
Step 3: Simplify and solve for the variable
5𝑥=10
𝑥=2 Divide by 5 to both sides
Step 4: Substitute the solved variable back into the original to get the other variable
3𝑥+4𝑦=18 First equation
3(2)+4𝑦=18 Substitute x=2
6+4𝑦=18
4𝑦=12 Subtract 6 to both sides
𝑦=3 Divide by 4 to both sides
The solution of a system is always in the format of an order pair
(2, 3) Solution
An order pair is ( 𝑥, 𝑦)

25. Practice on solving a system by Elimination
3𝑥+3𝑦=15 −2𝑥+3𝑦=−5

26. Practice on solving a system by Elimination
Step 1: check that the coefficient of the one of the variable are opposites. 3𝑥+3𝑦=15 −2𝑥+3𝑦=−5 Step 1b: 3𝑥+3𝑦=15 −1(−2𝑥+3𝑦=−5) Result 3𝑥+3𝑦=15 2𝑥−3𝑦=5

27. 3𝑥+3𝑦 = 15 2𝑥−3𝑦 = 5 5𝑥 =20 (4, 1) Solution An order pair is ( 𝑥, 𝑦)
Step 2: Add the two equations together (one variable should disappear)
3𝑥+3𝑦 = 𝑥−3𝑦 = 5 5𝑥 =20
Step 3: Simplify and solve for the variable
5𝑥=20
𝑥=4 Divide by 5 to both sides
Step 4: Substitute the solved variable back into the original to get the other variable
3𝑥+3𝑦=15 First equation
3(4)+3𝑦=15 Substitute x=4
12+3𝑦=15
3𝑦=3 Subtract 12 to both sides
𝑦=1 Divide by 4 to both sides
The solution of a system is always in the format of an order pair
(4, 1) Solution
An order pair is ( 𝑥, 𝑦)

28. Thursday 01/24/19 Homework solution
Solve the system of equation by elimination 1.
7𝑥+4𝑦=2 9𝑥−4𝑦=30
Solve by elimination because the coefficient of y are opposite
Step 1: check that the coefficient of the one of the variable are opposites.
7𝑥+4𝑦=2 9𝑥−4𝑦=30
Step 2: Add the two equations together (one variable should disappear)
7𝑥+ 4𝑦 = 2 9𝑥 −4𝑦 = 𝑥 =32
Step 3: Simplify and solve for the variable
16𝑥=32
𝑥=2 Divide by 16 to both sides

29. Correct order pair (2, −3) An order pair is ( 𝑥, 𝑦)
Step 4: Substitute the solved variable back into the original to get the other variable 7𝑥+4𝑦=2 First equation 7(2)+4𝑦=2 Substitute x=2 14+4𝑦=2 4𝑦=−12 Subtract 14 to both sides 𝑦=−3 Divide by 4 to both sides
The solution of a system is always in the format of an order pair
Correct order pair (2, −3)
An order pair is ( 𝑥, 𝑦)

30. Thursday 01/24/19 Homework solution
Solve the system of equation by elimination 2.
3𝑥−4𝑦=−5 5𝑥−2𝑦=−6
Solve by elimination because the coefficient of y are opposite
Step 1: check that the coefficient of one of the variables are opposites.
They are not, so we need to make one of them something else
3𝑥−4𝑦=−5 −𝟐∙(5𝑥−2𝑦=−6) Multiple the second equation by -2
Step 1 again: check that the coefficient of the one of the variables are opposites.
3𝑥−4𝑦=−5 −10𝑥+4𝑦=12) We are good now
Step 2: Add the two equations together (one variable should disappear)
3𝑥 + −4𝑦 = −5 −10𝑥 +4𝑦 =12 −7𝑥 =7
Step 3: Simplify and solve for the variable
−7𝑥=7
𝑥=−1 Divide by -7 to both sides

31. Correct order pair (−1, 1 2 ) An order pair is ( 𝑥, 𝑦)
Step 4: Substitute the solved variable back into the original to get the other variable 3𝑥−4𝑦=−5 First equation 3(−1)−4𝑦=−5 Substitute x=−1 −3−4𝑦=−5 −4𝑦=−2 Add 3 to both sides 𝑦= 2 4 𝑜𝑟 1 2 Divide by -4 to both sides
The solution of a system is always in the format of an order pair
Correct order pair (−1, 1 2 )
An order pair is ( 𝑥, 𝑦)

32. Thursday 01/24/19 Homework solution
Solve the system of equation by elimination 3.
2𝑥+3𝑦=8 3𝑥+2𝑦=7
Solve by elimination because the coefficient of y are opposite
Step 1: check that the coefficient of one of the variables are opposites.
They are not, so we need to make both of them something else
𝟑∙ 2𝑥+3𝑦=8 Multiple the first equation by 3 −𝟐∙ 3𝑥+2𝑦=7 Multiple the second equation by −2
Step 1 again: check that the coefficient of the one of the variables are opposites.
6𝑥+9𝑦=24 −6𝑥−4𝑦=−14 We are good now
Step 2: Add the two equations together (one variable should disappear)
6𝑥+9𝑦=24 −6𝑥−4𝑦=−14 5𝑦 =10
Step 3: Simplify and solve for the variable
5𝑦=10
𝑦=2 Divide by 5 to both sides

33. Correct order pair (1, 2) An order pair is ( 𝑥, 𝑦)
Step 4: Substitute the solved variable back into the original to get the other variable 2𝑥+3𝑦=8 First equation 2𝑥+3(2)=8 Substitute y=2 2𝑥+6=8 2𝑥=2 Subtract 6 to both sides 𝑥=1 Divide by 2 to both sides
The solution of a system is always in the format of an order pair
Correct order pair (1, 2)
An order pair is ( 𝑥, 𝑦)

34. 5.3 Solve System by Elimination Day 3 Date 1/25/19
Turn in your homework to the back table.
Copy down Essential Question.
Work on Warm Up.
Essential Question
Why do the coefficient in a system of equation need to be opposite values of each other?
Warm Up: Add the two equation in each problem. 1.
−𝑥 +𝑦=5 𝑥−5𝑦=−9 2.
𝑥−10𝑦=60 𝑥+14𝑦=12 3.
2𝑥+3𝑦=12 5𝑥−𝑦=13
−4𝑦=−4
2𝑥+4𝑦=72
7𝑥+2𝑦=25

35. Exploration activity: Solving by Elimination2.
1𝑥−10𝑦=60 1𝑥+14𝑦=12 2x + 4y = 72 2.
𝑥−10𝑦=60 𝑥+14𝑦=12 2x + 4y = 72 3.
2𝑥+3𝑦=12 5𝑥−1𝑦=13 7x + 2y = 25 3.
2𝑥+3𝑦=12 5𝑥−1𝑦=13 7x + 2y = 25
Step 1: check that the coefficient of the one of the variable are opposites.
Step 1: check that the coefficient of the one of the variable are opposites.
Step 1b: multiple by a -1 to get the opposite value.
Step 1b: multiple by a -1 to get the opposite value.
2𝑥+3𝑦=12 −1∙(5𝑥−1𝑦=13)
1𝑥−10𝑦=60 −1∙(1𝑥+14𝑦=12)
2𝑥+3𝑦=12 −5𝑥+1𝑦=−13
2𝑥+3𝑦=12 −5𝑥+1𝑦=−13
1𝑥−10𝑦=60 −1𝑥−14𝑦=−12
1𝑥−10𝑦=60 −1𝑥−14𝑦=−12
Step 1: check that the coefficient of the one of the variable are opposites.
Step 1: check that the coefficient of the one of the variable are opposites.

36. How to Solve by Elimination by multiplying first
2𝑥+3𝑦=12 5𝑥−1𝑦=13
Step 1: check that the coefficient of the one of the variable are opposites.
2𝑥+3𝑦=12 5𝑥−1𝑦=13
Step 1b: multiple by (something) to get the opposite value.
2𝑥+3𝑦=12 3∙(5𝑥−𝑦=13)
Multiple by 3 to the second equation
2𝑥+3𝑦=12 15𝑥−3𝑦=39
Step 1: check that the coefficient of the one of the variable are opposites.
2𝑥+3𝑦=12 15𝑥−3𝑦=39

37. 2𝑥 + 3𝑦 = 12 15𝑥 − 3𝑦 = 39 17𝑥 = 51 (3, 2) Solution
Step 2: Add the two equations together (one variable should disappear)
2𝑥 + 3𝑦 = 12 15𝑥 − 3𝑦 = 𝑥 = 51
Step 3: Simplify and solve for the variable
17𝑥=51
𝑥=3 Divide by 17 to both sides
Step 4: Substitute the solved variable back into the original to get the other variable
2𝑥+3𝑦=12 First equation
2(3)+3𝑦=12 Substitute x=3
6+3𝑦=12
3𝑦=6 Subtract 6 to both sides
𝑦=2 Divide by 3 to both sides
The solution of a system is always in the format of an order pair
(3, 2) Solution
An order pair is ( 𝑥, 𝑦)

38. or Practice on solving by Elimination by multiplying first
2𝑥+𝑦=3 𝑥−3𝑦=12
Step 1: check that the coefficient of the one of the variable are opposites.
2𝑥+𝑦=3 1𝑥−3𝑦=12 or
2𝑥+1𝑦=3 1𝑥−3𝑦=12
Step 1b: multiple by (something) to get the opposite value.
2𝑥+𝑦=3 −2∙(1𝑥−3𝑦=12)
Multiple by -2 to the second equation
2𝑥+𝑦=3 −2𝑥+6𝑦=−24
Step 1: check that the coefficient of the one of the variable are opposites.
2𝑥+𝑦=3 −2𝑥+6𝑦=−24

39. 2𝑥 + 𝑦 =3 −2𝑥 + 6𝑦 =−24 7𝑦=−21 (3, −3) Solution
Step 2: Add the two equations together (one variable should disappear)
2𝑥 + 𝑦 =3 −2𝑥 + 6𝑦 =−24 7𝑦=−21
Step 3: Simplify and solve for the variable
7𝑦=−21
𝑦=−3 Divide by 7 to both sides
Step 4: Substitute the solved variable back into the original to get the other variable
2𝑥+𝑦=3 First equation
2𝑥+ −3 =3 Substitute y=−3
2x−3 =3
2𝑥=6 Add 3 to both sides
𝑥=3 Divide by 2 to both sides
The solution of a system is always in the format of an order pair
(3, −3) Solution
An order pair is ( 𝑥, 𝑦)

40. Math Talk
Which is incorrect? Explain the error