1. 5.1 Solve System by graphing day 3 Date 1/14/19
Copy down Essential Question.
Work on Warm Up.
Essential Question
Why can we call the solution to a system of equation the break even or the tie point?
Warm Up:
Find the slope and the y-intercept in each equation
1. 𝑦=− 3 5 𝑥+1
2. 𝑦=−𝑥
3. 𝑦− 1 2 𝑥=4
𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 =1 slope= − 3 5
𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 =0 slope= − 1 1
𝑦−𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 =4 slope= 1 2

2. Practice: Solve system by graphing
Review Problem
Solve the system by graphing. Check your answer.
𝒚 = – 𝟓 𝟑 𝒙 –+𝟑
Graph the system.
Find the slope and the y-intercept in each equation
𝒚 = 𝟏 𝟑 𝒙 −𝟑
The solution is (–2, 3).

3. Application Example 1
Wren and Jenni are reading the same book. Wren is on page 14 and reads 2 pages every night. Jenni is on page 6 and reads 3 pages every night. After how many nights will they have read the same number of pages? How many pages will that be?

4. Understand the Problem1
Understand the Problem
The answer will be the number of nights it takes for the number of pages read to be the same for both girls.
List the important information:
Wren on page 14 Reads 2 pages a night
Jenni on page Reads 3 pages a night

5. 2
Make a Plan
Write a system of equations, one equation to represent the number of pages read by each girl. Let x be the number of nights and y be the total pages read.
Total
pages is
number read
every
night
plus
already read.
Wren y = 2
 x + 14
Jenni y = 3
 x + 6

6. Solve 3
Graph y = 2x + 14 and y = 3x + 6. The lines appear to intersect at (8, 30). So, the number of pages read will be the same at 8 nights with a total of 30 pages. 
(8, 30)
Nights

7.   Look Back Check (8, 30) using both equations.4
Check (8, 30) using both equations.
Number of days for Wren to read 30 pages.
2(8) + 14 = = 30 
Number of days for Jenni to read 30 pages.
3(8) + 6 = = 30 

8. Application Example 2
Video club A charges $10 for membership and $3 per movie rental. Video club B charges $15 for membership and $2 per movie rental. For how many movie rentals will the cost be the same at both video clubs? What is that cost?

9. Understand the Problem1
Understand the Problem
The answer will be the number of movies rented for which the cost will be the same at both clubs.
List the important information:
Rental price: Club A $3 Club B $2
Membership: Club A $10 Club B $15

10. 2
Make a Plan
Write a system of equations, one equation to represent the cost of Club A and one for Club B. Let x be the number of movies rented and y the total cost.
Total
cost is
price
for each
rental
plus
member-
ship fee.
Club A y = 3
 x + 10
Club B y = 2
 x + 15

11. Solve 3
Graph y = 3x + 10 and y = 2x The lines appear to intersect at (5, 25). So, the cost will be the same for 5 rentals and the total cost will be $25.

12.   Look Back Check (5, 25) using both equations.4
Check (5, 25) using both equations.
Number of movie rentals for Club A to reach $25:
3(5) + 10 = = 25 
Number of movie rentals for Club B to reach $25:
2(5) + 15 = = 25 

13. 5.2 Solve System by Substitution Date 1/15/19
Copy down Essential Question.
Work on Warm Up.
Essential Question
Why do you need two equations when trying to solve for two variables?
Warm Up: Explain the word
Word: Substitute
Used it in a sentence and give one explain of how we use it in math.

14. Why can’t you solve 3𝑥+2𝑦=4 ?
There is only 1 equation for 2 variable.
You can you solve 2𝑦=4
There is 1 equation for 1 variable.
For 3𝑥+2𝑦=4 ?How many equation do we need?
There is 2 equation for 2 variable.

15. Rule of Linear Algebra
There must be an equal amount of variable “unknowns” as equations for there to be a solution “ intersection” .
Example. one equation, one unknown.
two equations, two unknowns.
three equations, three unknowns.

16. Example 1 : Solving a System of Linear Equations by Substitution
Solve the system by substitution.
y = 3x
y = x – 2
Step 1 y = 3x
Both equations are solved for y.
y = x – 2
Step 2 y = x – 2
3x = x – 2
Substitute 3x for y in the second equation.
Step 3
–x –x
2x = –2
2x = –2
x = –1
Solve for x. Subtract x from both sides and then divide by 2.

17.   Example 1 Continued Solve the system by substitution.
Write one of the original equations.
Step 4
y = 3x
y = 3(–1)
y = –3
Substitute –1 for x.
Write the solution as an ordered pair.
Step 5
(–1, –3)
Check Substitute (–1, –3) into both equations in the system.
y = 3x
–3 3(–1)
–3 –3 
y = x – 2
–3 –1 – 2
–3 –3 

18. Example 1b : Solving a System of Linear Equations by Graphing
Solve the system by graphing.
y = 3x
y = x – 2

19. 5.2 Solve System by Substitution Date 1/15/19
Copy down Essential Question.
Copy down and Work on Warm Up.
Essential Question
How does solving a system by substitute work? Explain the process in your own words.
Warm Up: Find the cost of 1 apple and 1 orange

20. Practice 1: Solving a System of Linear Equations by Substitution
Solve the system by substitution.
y = x + 1
4x + y = 6
The first equation is solved for y.
Step 1 y = x + 1
Step 2 4x + y = 6
4x + (x + 1) = 6
Substitute x + 1 for y in the second equation.
5x + 1 = 6
Simplify. Solve for x.
Step 3
–1 –1
5x = 5
x = 1
5x = 5
Subtract 1 from both sides.
Divide both sides by 5.

21.   Practice 1 Continued Solve the system by substitution.
Write one of the original equations.
Step 4
y = x + 1
y = 1 + 1
y = 2
Substitute 1 for x.
Write the solution as an ordered pair.
Step 5
(1, 2)
Check Substitute (1, 2) into both equations in the system.
y = x + 1
2 2 
4x + y = 6
4(1)
6 6 

22. Practice 2 : Solving a System of Linear Equations by Substitution
Solve the system by substitution.
x + 2y = –1
x = 5 + y
Step 1 x + 2y = –1
Solve the first equation for x by subtracting 2y from both sides.
(5+y) + 2y = –1
Step 2 x – y = 5
(–2y – 1) – y = 5
Substitute –2y – 1 for x in the second equation.
–3y – 1 = 5
Simplify.

23. Practice 2 Continued
Step 3
–3y – 1 = 5
Solve for y.
+1 +1
–3y = 6
Add 1 to both sides.
–3y = 6
–3 –3
y = –2
Divide both sides by –3.
Step 4
x – y = 5
Write one of the original equations.
x – (–2) = 5
x + 2 = 5
Substitute –2 for y.
–2 –2
x = 3
Subtract 2 from both sides.
Write the solution as an ordered pair.
Step 5 (3, –2)

24. Practice 3
Solve the system by substitution.
y = x + 3
y = 2x + 5
Step 1
y = x + 3
y = 2x + 5
Both equations are solved for y.
Step 2
2x + 5 = x + 3
y = x + 3
Substitute 2x + 5 for y in the first equation.
–x – 5 –x – 5
x = –2
Step 3
2x + 5 = x + 3
Solve for x. Subtract x and 5 from both sides.

25. Practice 3 Continued
Solve the system by substitution.
Write one of the original equations.
Step 4
y = x + 3
y = –2 + 3
y = 1
Substitute –2 for x.
Step 5
(–2, 1)
Write the solution as an ordered pair.

26. Example 2
Solve the system by substitution.
x = 2y – 4
x + 8y = 16
Step 1 x = 2y – 4
The first equation is solved for x.
(2y – 4) + 8y = 16
x + 8y = 16
Step 2
Substitute 2y – 4 for x in the second equation.
Step 3
10y – 4 = 16
Simplify. Then solve for y.
10y = 20
Add 4 to both sides.
10y =
Divide both sides by 10.
y = 2

27. Exmaple 2 Continued
Solve the system by substitution.
Step 4
x + 8y = 16
Write one of the original equations.
x + 8(2) = 16
Substitute 2 for y.
x + 16 = 16
Simplify.
x = 0
– 16 –16
Subtract 16 from both sides.
Write the solution as an ordered pair.
Step 5 (0, 2)

28. Practice 4
Solve the system by substitution.
2x + y = –4
x + y = –7
Solve the second equation for x by subtracting y from each side.
Step 1 x + y = –7
– y – y
x = –y – 7
2(–y – 7) + y = –4
x = –y – 7
Step 2
Substitute –y – 7 for x in the first equation.
2(–y – 7) + y = –4
Distribute 2.
–2y – 14 + y = –4

29. Practice 4 Continued
Step 3
–2y – 14 + y = –4
Combine like terms.
–y – 14 = –4
–y = 10
Add 14 to each side.
y = –10
Step 4
x + y = –7
Write one of the original equations.
x + (–10) = –7
Substitute –10 for y.
x – 10 = – 7

30. Practice 4 Continued
Step 5
x – 10 = –7
Add 10 to both sides.
x = 3
Step 6
(3, –10)
Write the solution as an ordered pair.

31. Tuesday 01/15/19 Homework Solution1.
x =5
y = 2x-3
Step 1 x=5
The first equation is solved for x.
Step 2
y = 2(5)-3
y = 2x-3
Substitute x=5 for x in the second equation.
Simplify.
Step 3
y = 10-3
y = 7
Write the solution as an ordered pair.
Step 4
(5, 7)

32. Tuesday 01/15/19 Homework Solution2.
x =y + 2
y = 2x-3
Step 1 x=y+2
The first equation is solved for x.
Step 2
y = 2(y+2)-3
y = 2x-3
Substitute x=y +2 for x in the second equation.
Simplify.
Step 3
y = 2y
y = 2y +1
-2y -2y
-1y = 1
y = -1

33. x =y + 2
Step 4
Substitute y = -1 for y back into the first equation.
x =(-1) + 2
x = 1
Write the solution as an ordered pair.
Step 5
(1, -1)

34. Tuesday 01/15/19 Homework Solution3.
2x-3y=7
y=3x-7
Step 1 y=3x-7
The second equation is solved for x.
Step 2
Substitute y = 3x-7 for u in the first equation.
2x - 3y =7
2x-3(3x-7) =7
2x-9x+21=7
Combine like terms
Step 3
-7x+21=7
Simplify
-7x=-14
−𝟕𝒙 −𝟕 = −𝟏𝟒 −𝟕
x=2

35. Step 4
y= 3x -7
Substitute x = 2 for y back into the second equation.
y=3(2)-7
y=6-7
y=-1
Write the solution as an ordered pair.
Step 5
(2, -1)

36. Wednesday 01/16/19 Homework Solution
1. 𝑥=−5 𝑦=2𝑥−3
Step 1
𝑥=−5
The first equation is solved for x.
Step 2
𝑦=2𝑥−3
substitute 𝑥=−5 into the second equation
𝑦=2(−5)−3
Step 3
simplify to solve for y
𝑦=−10−3
𝑦=−13
Step 4
(−5, −13)
write the solution as an order pair.

37. Wednesday 01/16/19 Homework Solution
2. 𝑥=−𝑦+2 𝑦=2𝑥−2
Step 1
𝑥=−𝑦+2
The first equation is solved for x.
Step 2
𝑦=2𝑥−2
substitute 𝑥=−𝑦+2 into the second equation
𝑦=2(−𝑦+2)−2
Step 3
𝑦=−2𝑦+4−2
simplify to solve for y
𝑦=−2𝑦+2
+2𝑦 +2𝑦
3𝑦=2
3𝑦 3 = 2 3
𝑦= 2 3

38. Step 4
𝑥=−𝑦+2
substitute 𝑦= 2 3 into the first equation
𝑥=−( 2 3 )+2
𝑥= 4 3
Step 5
( 4 3 , 2 3 )
write the solution as an order pair.

39. Wednesday 01/16/19 Homework Solution
3. 3𝑥+𝑦=9 𝑦=2𝑥+4
Step 1
𝑦=2𝑥+4
The second equation is solved for y.
substitute 𝑦=2𝑥+4 into the first equation
Step 2
3𝑥+𝑦=9
3𝑥+(2𝑥+4)=9
Step 3
3𝑥+2𝑥+4=9
simplify to solve for x
5𝑥+4=9
−4 −4
5𝑥=5
5𝑥 5 = 5 5
𝑥=1

40. Step 4
𝑦=2𝑥+4
substitute x=1 into the second
equation and solved for y.
𝑦=2(1)+4
𝑦=2+4
𝑦=6
Step 5
(1, 6)
write the solution as an order pair.

41. Thursday 01/17/19 Homework Solution
1. 𝑥−𝑦=2 𝑦−2𝑥=−3
Pre Step 1
𝑥−𝑦=2
do some algebra to solve for x
+𝑦 +𝑦
𝑥=𝑦+2
Step 1
𝑦−2𝑥=−3
substitute x=y+2 into the second equation
𝑦−2(𝑦+2)=−3
Step 2
𝑦−2𝑦−4=−3
simplify to solve for y
−1𝑦−4=−3
−1𝑦=1
𝑦=−1

42. Step 3
𝑥=𝑦+2
substitute y=−1 into the first
equation and solved for x.
𝑥= −1 +2
𝑥=1
Step 4
(1, −1)
write the solution as an order pair.

43. Thursday 01/17/19 Homework Solution
2. 2𝑥−3𝑦=7 𝑦−3𝑥=−7
Pre Step 1
𝑦−3𝑥=−7
do some algebra to solve for x
+3𝑥 +3𝑥
𝑦=3𝑥−7
Step 1
2𝑥−3𝑦=7
substitute y=3x−7 into the first equation
2𝑥−3(3x−7)=7
Step 2
2𝑥−9𝑥+21=7
simplify to solve for x
−7𝑥+21=7
−21 −21
−7𝑥=−14
−7𝑥 −7 = −14 −7
𝑥=2

44. Step 3
𝑦−3𝑥=−7
substitute x=2 into the first
equation and solved for x.
y−3(2)=−7
y−6=−7
𝑦=−1
𝑦=−1
Step 4
(2, −1)
write the solution as an order pair.

45. Thursday 01/17/19 Homework Solution
3. 𝑥+𝑦=2 𝑦−2𝑥=−2
Pre Step 1
𝑥+𝑦=2
do some algebra to solve for y
−𝑥 −𝑥
𝑦=−𝑥+2
Step 1
𝑦−2𝑥=−2
substitute y=−x+2 into the first equation
(−x+2)−2𝑥=−2
Step 2
−𝑥+2−2𝑥=−2
simplify to solve for x
2−3𝑥=−2
− −2
−3𝑥=−4
−3𝑥 −3 = −4 −3
𝑥= 4 3

46. substitute 𝑥= 4 3 into the first
equation and solved for x.
Step 3
𝑥+𝑦=2
( 4 3 )+𝑦=2
− − 4 3
𝑦= 2 3
Step 5
( 4 3 , 2 3 )
write the solution as an order pair.

47. .Make sure you submit the test when done.
State Test Day Date 1/18/19
Drop off your homework to the back table
Log into a laptop
Cick on the CAASPP icon
Log in with the info on the card I give you
SESSION ID:
.Make sure you submit the test when done.
I will give out a card with your log in info
*no notes
*you can use scratch paper
*you can have all the time you need, but only TODAY
* this goes in the grade as a test score