1. Today’s Agenda
E – How do you rewrite equations from standard form to slope-intercept form?
A - Warm-up: Writing systems equations
Journal: Describe 2 ways to graph a line
Review: Looking at y=mx+b
T - New: Rewriting equations from standard to slope-intercept form (graphic organizer)
Classwork: Racing Game
S – Journal writing to answer LEQ
Homework: Rewriting Equations worksheet
12/29/2018
Geometry CP

2. JOURNAL TIME (8 mins) 
Directions: Write down the journal prompt and then answer
Describe the 2 different ways to graph a line that we have learned in class so far (Be specific)
Which way do you prefer and why?
12/29/2018
Geometry CP

3. Lesson Essential Question:
Rewriting Equations 
Lesson Essential Question:
How do you rewrite equations from standard form to graphing form?
Write LEQ in journal
12/29/2018
Geometry CP

4. 2 Forms of Linear Equations 
The forms of linear equations are the formats in which the information is written in.
These two forms are the most commonly used ways to write linear equations.
1. Standard Form: Ax + By =C
2. Slope Intercept Form: y=mx+b
Write 2 forms of linear equations in journal
12/29/2018
Geometry CP

5. Important!!! 
This is one of the BIG concepts you learned in Math 8 and Algebra I. You need to thoroughly understand this!
Slope – Intercept Form
y = mx + b
m represents the slope
b represents the y-intercept
Write in journal
12/29/2018
Geometry CP

6. Review: -Writing Equations Given Slope & Y-intercept
Write the equation of a line that has a y-intercept of - 3 and a slope of - 4.
y = -3x – 4
y = -4x – 3
y = -3x + 4
y = -4x + 3
12/29/2018
Geometry CP

7. Review: Find the slope and y-intercept of y = 4 – 2x
m = 2; b = 4
m = 4; b = 2
m = -2; b = 4
m = 4; b = -2
12/29/2018
Geometry CP

8. Standard Form to Slope Intercept Form
Ax + By = C to
y = mx + b
12/29/2018
Geometry CP

9. What is Standard Form  Standard Form is Ax + By = C
Basically, if your x and y are on the same side of the equation, then it is in standard form.
Write in journal
12/29/2018
Geometry CP

10. Identify the equations in standard form
A. 2x – 4y = 6 B. y = 3x + 1 C. x – y = 1 D. 4y = 5x + 8 E. -x + 2y = 6 F. y = 1/3x G. 2y +7 = 3x
12/29/2018
Geometry CP

11. Converting from standard form (Ax + By = C) to slope-intercept form (y = mx + b)
Tape in journal
12/29/2018
Geometry CP

12. Converting Standard to Slope-Intercept form
2x + 3y = 6
ax + by = c
(Standard Form)
-2x
-2x
WE WANT THIS FORM!!!
3y = 6 - 2x 3
y = 2 - 2 3 x
y = 2 3 x
y = mx + b
(Slope- Intercept)
12/29/2018
Geometry CP

13. 3 Powerful Moves to get your equation into y=
6X + 4Y = 12
MOVE X
DROP ALL
DIVIDE ALL
12/29/2018
Geometry CP

14. 3 Powerful Moves to get your equation into y=
6X + 4Y = 12
6X + 4Y = 12 -6x -6x
MOVE X
Add or Subtract the x term to the other side of equals.
12/29/2018
Geometry CP

15. 3 Powerful Moves to get your equation into y=
6X + 4Y = 12
6X + 4Y = 12
-6x x
4y = 12 -6x
2. DROP ALL
Bring all terms down in order.
Do not add or subtract unlike terms!!!
12/29/2018
Geometry CP

16. 3 Powerful Moves to get your equation into y=
6X + 4Y = 12
6X + 4Y = 12
-6x x
4y = 12 -6x
y= 3 – 3/2 x
3. DIVIDE ALL
Divide each term by the number attached to y
keep slope a fraction!
12/29/2018
Geometry CP

17. 3 Powerful Moves to get your equation into y=
-4X + 3Y = 12
MOVE X
DROP ALL
DIVIDE ALL
12/29/2018
Geometry CP

18. 3 Powerful Moves to get your equation into y=
-4X + 3Y = 12
-4X + 3Y = 12 +4x +4x
MOVE X
Add or Subtract the x term to the other side of equals.
12/29/2018
Geometry CP

19. 3 Powerful Moves to get your equation into y=
-4X + 3Y = 12
-4X + 3Y = 12
+4x x
3y = 12 +4x
2. DROP ALL
Bring all terms down in order.
Do not add or subtract unlike terms!!!
12/29/2018
Geometry CP

20. 3 Powerful Moves to get your equation into y=
-4X + 3Y = 12
-4X + 3Y = 12
+4x x
3y = 12 +4x
y= 4 + 4/3 x
3. DIVIDE ALL
Divide each term by the number attached to y
keep slope a fraction!
12/29/2018
Geometry CP

21. The 3 Power Moves to getting lines into y = form.1. 2. 3.
MOVE the x term by Adding/Subtracting!
Write in journal
Drop ALL!
Divide ALL!
12/29/2018
Geometry CP

22. Pair Race Directions
Equations are going to flash on the screen. The first one to step forward and describe the first step to converting the equation will earn the point.
First person to answer correctly wins!
Everyone….Please pay attention 
12/29/2018
Geometry CP

23. Example 3x + 2y = 18 That would look like: 3x + 2y = 18 -3x -3x
The first step is: Subtract 3x from both sides
That would look like:
3x + 2y = 18
-3x x
2y = 18 – 3x
12/29/2018
Geometry CP

24. Example -7x + 14y = 28 That would look like: -7x + 14y = 28 +7x +7x
The first step is: Add 7x to both sides
That would look like:
-7x + 14y = 28
+7x x
14y = x
12/29/2018
Geometry CP

25. Let’s Race!
As quickly and quietly as possible line up please!
No hitting, touching, pushing, poking…just get in line!
Ready, Set, GO!!
12/29/2018
Geometry CP

26. Correct! Subtract 4x from both sides!!
4x + 5y = 10
Correct! Subtract 4x from both sides!!
Great Job!
4x + 5y = 10
-4x x
5y = 10 – 4x
12/29/2018
Geometry CP

27. Correct! Add 6x to both sides!!
-6x + 3y = 12
Correct! Add 6x to both sides!!
Great Job!
-6x + 3y = 12
+6x x
3y = x
12/29/2018
Geometry CP

28. Correct! Subtract 9x from both sides!!
9x - y = -8
Correct! Subtract 9x from both sides!!
Great Job!
9x - y = -8
-9x x
- y = -8 – 9x
12/29/2018
Geometry CP

29. Correct! Subtract 10x from both sides!!
10x - 20y = 20
Correct! Subtract 10x from both sides!!
Great Job!
10x - 20y = 20
-10x x
-20y = 20 – 10x
12/29/2018
Geometry CP

30. Correct! Add 11x to both sides!!
-11x + 11y = 33
Correct! Add 11x to both sides!!
Great Job!
-11x + 11y = 33
+11x x
11y = x
12/29/2018
Geometry CP

31. Correct! Add 4x to both sides!!
-4x + 2y = 8
Correct! Add 4x to both sides!!
Great Job!
-4x + 2y = 8
+4x x
2y = 8 + 4x
12/29/2018
Geometry CP

32. Correct! Add 8x to both sides!!
-8x - 4y = -16
Correct! Add 8x to both sides!!
Great Job!
-8x - 4y = -16
+8x x
-4y = x
12/29/2018
Geometry CP

33. Correct! Subtract 7x from both sides!!
7x + y = -2
Correct! Subtract 7x from both sides!!
Great Job!
7x + y = -2
-7x x
y = -2 – 7x
12/29/2018
Geometry CP

34. Correct! Subtract 2x from both sides!!
2x + 2y = 10
Correct! Subtract 2x from both sides!!
Great Job!
2x + 2y = 10
-2x x
2y = 10 – 2x
12/29/2018
Geometry CP

35. Correct! Add 5x to both sides!!
-5x + 3y = -9
Correct! Add 5x to both sides!!
Great Job!
-5x + 3y = -9
+5x x
3y = x
12/29/2018
Geometry CP

36. Correct! Add 8x to both sides!!
-8x - 4y = 24
Correct! Add 8x to both sides!!
Great Job!
-8x - 4y = 24
+8x x
-4y = x
12/29/2018
Geometry CP

37. Correct! Subtract 6x from both sides!!
6x – 12y = -36
Correct! Subtract 6x from both sides!!
Great Job!
6x – 12y = -36
-6x x
-12y = -36 – 6x
12/29/2018
Geometry CP

38. Correct! Add 2x to both sides!!
-2x – 2y = -14
Correct! Add 2x to both sides!!
Great Job!
-2x – 2y = -14
+2x x
-2y = x
12/29/2018
Geometry CP

39. GREAT GAME!!!!
Please go back to your seats, we are going to return to our notes and get this first step written down and committed to memory 
12/29/2018
Geometry CP

40. First Step Example Problem 1
6x + 3y = 9
12/29/2018
Geometry CP

41. First Step Example Problem 2
-10x + 2y = 8
12/29/2018
Geometry CP

42. First Step Example Problem 3
x - 2y = 4
12/29/2018
Geometry CP

43. First Step Example Problem 4
-x + y = -2
12/29/2018
Geometry CP

44. First Step Example Problem 5
-8x – 2y = -2
12/29/2018
Geometry CP

45. Your Turn
With your shoulder buddy, complete the 10 problems on the next page.
Remember, you are only showing the first step!
You have 5 minutes to get this completed 
While students are working on the 10 problems – write the problems on the board so that the students can come up and put their work on the board. All 10 on the board at once. With those 10 – show the process of the second step. Have the students just watch and help as you solve them. They should be watching – not writing anything down.
12/29/2018
Geometry CP

46. Pair Race Directions
Equations are going to flash on the screen. The first one to step forward and show the first AND second steps to converting the equation will win.
Circle the slope and square on y-intercept
What ever side of the room has the most points wins!
EVERYONE….Please pay attention 
12/29/2018
Geometry CP

47. Example 4x + 2y = 18 Final Result: y = 9 – 2x That would look like:
The first step is: Subtract 4x from both sides
That would look like:
4x + 2y = 18
-4x x
2y = 18 – 4x
The second step is: Divide everything by 2
2y = 18 – 4x 2 2 2
Final Result: y = 9 – 2x
12/29/2018
Geometry CP

48. Example -14x + 7y = 28 Final Result: y = 4 + 2x That would look like:
The first step is: Add 14x to both sides
That would look like:
-14x + 7y = 28
+14x x
7y = x
The second step is: Divide everything by 7
7y = x 7 7 7
Final Result: y = 4 + 2x
12/29/2018
Geometry CP

49. Example -8x – 2y = -10 Final Result: y = 5 – 4x That would look like:
The first step is: Add 8x to both sides
That would look like:
-8x – 2y = -10
+8x x
-2y = x
The second step is: Divide everything by -2
-2y = x -2 -2 -2
Final Result: y = 5 – 4x
12/29/2018
Geometry CP

50. Example 12x – 6y = 18 Final Result: y = -3 + 2x That would look like:
The first step is: Subtract 12x from both sides
That would look like:
12x – 6y = 18
-12x x
-6y = 18 – 12x
The second step is: Divide everything by -6
-6y = 18 – 12x -6 -6 -6
Final Result: y = x
12/29/2018
Geometry CP

51. Let’s Race Again!
ReadySet GO!!
12/29/2018
Geometry CP

52. 4x + 5y = 10 4x + 5y = 10 -4x -4x 5y = 10 – 4x First Step?
Correct! Subtract 4x from both sides!!
4x + 5y = 10
-4x x
5y = 10 – 4x
Second Step?
Correct! Divide everything by 5!!
12/29/2018
Geometry CP

53. 5y = 10 – 4x
y = 2 – 4/5x
12/29/2018
Geometry CP

54. Correct! Add 6x to both sides!! Correct! Divide everything by 3!!
-6x + 3y = 12
Correct! Add 6x to both sides!!
-6x + 3y = 12
+6x x
3y = x
Second Step?
Correct! Divide everything by 3!!
12/29/2018
Geometry CP

55. 3y = x
y = 4 +2x
12/29/2018
Geometry CP

56. 9x - y = -8 9x - y = -8 -9x -9x - y = -8 – 9x - 1y = -8 – 9x
Correct! Subtract 9x from both sides!!
9x - y = -8
-9x x
- y = -8 – 9x
What’s in front of the y…that is always there…we just don’t write it (because mathematicians are lazy )?
- 1y = -8 – 9x
Second Step?
Correct! Divide everything by -1!!
12/29/2018
Geometry CP

57. -y = -8 – 9x
y = 8 +9x
12/29/2018
Geometry CP

58. 10x - 20y = 20
Correct! Subtract 10x from both sides!!
10x - 20y = 20
-10x x
-20y = 20 – 10x
Second Step?
Correct! Divide everything by -20
12/29/2018
Geometry CP

59. -20y = 20 – 10x
y = /2x
12/29/2018
Geometry CP

60. Correct! Add 11x to both sides!! Correct! Divide everything by 11
-11x + 11y = 33
Correct! Add 11x to both sides!!
-11x + 11y = 33
+11x x
11y = x
Second Step?
Correct! Divide everything by 11
12/29/2018
Geometry CP

61. 11y = x
y = 3 +x
12/29/2018
Geometry CP

62. Correct! Add 4x to both sides!! Correct! Divide everything by 2
-4x + 2y = 8
Correct! Add 4x to both sides!!
-4x + 2y = 8
+4x x
2y = 8 + 4x
Second Step?
Correct! Divide everything by 2
12/29/2018
Geometry CP

63. 2y = 8 + 4x
y = 4 +2x
12/29/2018
Geometry CP

64. Correct! Add 8x to both sides!! Correct! Divide everything by -4!!
-8x - 4y = -16
Correct! Add 8x to both sides!!
-8x - 4y = -16
+8x x
-4y = x
Second Step?
Correct! Divide everything by -4!!
12/29/2018
Geometry CP

65. -4y = x
y = x
12/29/2018
Geometry CP

66. 7x + y = -2
Correct! Subtract 7x from both sides!!
7x + y = -2
-7x x
y = -2 – 7x
Second Step?
Correct! There is no second step!
It’s already solved for y 
12/29/2018
Geometry CP

67. y = x
y = x
12/29/2018
Geometry CP

68. 2x + 2y = 10
Correct! Subtract 2x from both sides!!
2x + 2y = 10
-2x x
2y = 10 – 2x
Second Step?
Correct! Divide everything by 2!!
12/29/2018
Geometry CP

69. 2y = 10 – 2x
y = 5 -x
12/29/2018
Geometry CP

70. Correct! Add 5x to both sides!! Correct! Divide everything by 3
-5x + 3y = -9
Correct! Add 5x to both sides!!
-5x + 3y = -9
+5x x
3y = x
Second Step?
Correct! Divide everything by 3
12/29/2018
Geometry CP

71. 3y = x
y = /3x
12/29/2018
Geometry CP

72. Correct! Add 8x to both sides!! Correct! Divide everything by -4
-8x - 4y = 24
Correct! Add 8x to both sides!!
-8x - 4y = 24
+8x x
-4y = x
Second Step?
Correct! Divide everything by -4
12/29/2018
Geometry CP

73. -4y = x
y = x
12/29/2018
Geometry CP

74. 6x – 12y = -36 6x – 12y = -36 -6x -6x -12y = -36 – 6x
Correct! Subtract 6x from both sides!!
6x – 12y = -36
-6x x
-12y = -36 – 6x
Second Step?
Correct! Divide everything by -12
12/29/2018
Geometry CP

75. -12y = -36 – 6x
y = 3 +1/2x
12/29/2018
Geometry CP

76. Correct! Add 2x to both sides!! Correct! Divide everything by -2
-2x – 2y = -14
Correct! Add 2x to both sides!!
-2x – 2y = -14
+2x x
-2y = x
Second Step?
Correct! Divide everything by -2
12/29/2018
Geometry CP

77. -2y = x
y = 7 - x
12/29/2018
Geometry CP

78. Putting it all Together First & Second Step Example Problem 1
35x + 7y = 49
12/29/2018
Geometry CP

79. Putting it all Together First & Second Step Example Problem 2
-20x – 5y = -30
12/29/2018
Geometry CP

80. Putting it all Together First & Second Step Example Problem 3
-6x + 3y = 24
12/29/2018
Geometry CP

81. Putting it all Together First & Second Step Example Problem 4
-x + 2y = 4
12/29/2018
Geometry CP

82. Putting it all Together First & Second Step Example Problem 5
x + y = 8
12/29/2018
Geometry CP

83. Putting it all Together First & Second Step Example Problem 6
x + 4y = 8
12/29/2018
Geometry CP

84. Your Turn
With your shoulder buddy, complete the 10 problems on the next page.
Remember, you are completing the entire problem to solve for y.
You have 10 minutes to get this completed 
While students are working on the 10 problems – write the problems on the board so that the students can come up and put their work on the board. All 10 on the board at once. With those 10 – show the process of the second step. Have the students just watch and help as you solve them. They should be watching – not writing anything down.
12/29/2018
Geometry CP

85. ERROR ANALYSIS Molly JARED 12x + 3y = 9 12x + 3y = 9 3y = 9 – 12x
Four students rewrote the equation 12x + 3y = 9 into slope-intercept form. Determine who did it correctly. If the student did it incorrectly, explain the mistake.
Molly
12x + 3y = 9
3y = 9 – 12x
y = 3 – 12x
JARED
12x + 3y = 9
3y = 9 – 12x
y = 3 – 4x
Mia
12x + 3y = 9
3y = 9 – 12x
y = 3 – 4x
y = 4x - 3
Ali
12x + 3y = 9
4x + y = 3
y = -4x + 3
12/29/2018
Geometry CP

86. Journal Time!!
What are the three power moves that get any standard form equation into slope- intercept form?
Write an example problem and rewrite it from standard form into slope-intercept form!
12/29/2018
Geometry CP

87. Homework! Complete the Slope Intercept and Standard Form wsht
12/29/2018
Geometry CP

88. Pick a partner activity (10 mins)
Pick a partner within your color group to work on the problem
Make sure that you work TOGETHER and CHECK EACH OTHER’S WORK.
This will be a graded assignment to earn bonus points on your quiz 
12/29/2018
Geometry CP

89. You have 2 minutes to find your partner!
Purple Group
Colette
Dan
Kayla
Sydni
Jonathan
Phil
Pink Group
Megan
Tyheim
Tiyana
Alisa
Courtney
Orange Group
Daysia
Taylor
Chris M
Shiela
Andy
Chris N
Ashley
Steven
12/29/2018
Geometry CP

90. Purple Group Directions: Finding X & Y intercepts
For the following problems find the x & y intercepts. Show work!
Don’t forget that the x intercept happens when y=0 and the y intercept happens when x=0
Write all intercepts as an ordered pair (x,y)
a. 2x – 3y = 12
b. 2x + 3y = 12
c. 3x – y = 6
d. y – x = 5
12/29/2018
Geometry CP

91. Orange Group Directions: Rewriting Equations
Rewrite each equation into slope-intercept form (y =mx+b)
Identify the slope and y-intercept
Show all work!
3x + 2y = 28
b) 5y = 15 – 2x
c) 3y + 9 = 2x
12/29/2018
Geometry CP

92. Pink Group Directions: Rewriting Equations a) x + y = 20 5x + 4y = 24
Rewrite each equation into slope-intercept form (y =mx+b)
Identify the slope and y-intercept
Don’t forget the 3 POWER steps..Use your notes if needed!
Show all work!
a) x + y = 20
5x + 4y = 24
3x – 2y = 12
12/29/2018
Geometry CP

93. 12/29/2018
Geometry CP

94. Solve Systems of Equations by the Graphing Method
Lesson Essential Question:
Describe the types of solutions a system of equations can have?
12/29/2018
Geometry CP

95. What is a system of equations?
A system of equations is when you have two or more equations using the same variables.
The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair.
When graphing, you will encounter three possibilities.
12/29/2018
Geometry CP

96. Intersecting Lines (One Solution)
The point where the lines intersect is your solution.
What is the solution?
The solution of this graph is (1, 2)
(1,2)
12/29/2018
Geometry CP

97. Find the solution to the following system using the Graphing Method
y = -2x + 4
y = x - 2
Graph both equations. I will graph using slope-intercept form.
Graph the y-intercept, then the slope.
y = -2x + 4
y –int. = (0, 4) and
Slope = -2/1 or 2/-1
y = x - 2
y – int. = (0, -2) and
Slope = 1/1 or -1/-1
12/29/2018
Geometry CP

98. Step 2: Graph the equations.
y = -2x + 4
y = x - 2
Where do the lines intersect?
(2, 0)
2x + y = 4
x – y = 2
12/29/2018
Geometry CP

99. Step 3: Check your answer!
To check your answer, plug the point back in for x and y into both equations and simplify.
y = -2x + 4
(0) = -2(2) + 4
0 =
0 = 0
y = -x + 2
(0) = -(2) + 2
Nice job…let’s look how to solve it using
the graphing calculator!
12/29/2018
Geometry CP

100. Quick Stop & Jot DO ALL LINES ALWAYS HAVE A POINT OF INTERSECTION?
WHAT OTHER TYPES OF SOLUTIONS CAN SYSTEMS OF EQUATIONS HAVE?
12/29/2018
Geometry CP

101. Another type of solution
How would you describe these lines?
Y = 3x + 2
Y = 3x - 4
What do you think the solution, or point of intersection, is?
12/29/2018
Geometry CP

102. Parallel Lines (No Solution)
These lines never intersect!
Since the lines never cross, there is NO SOLUTION!
Parallel lines have the same slope with different y-intercepts.
12/29/2018
Geometry CP

103. Find the solution to the following system by the Graphing Method
y = 2x – 3
y = 2x + 1
Graph both equations using slope and y-intercept.
12/29/2018
Geometry CP

104. Step 2: Graph the equations.
y = 2x – 3
m = 2 and b = -3
y = 2x + 1
m = 2 and b = 1
Where do the lines intersect?
No solution!
Notice that the slopes are the same with different y-intercepts. If you recognize this early, you don’t have to graph them!
12/29/2018
Geometry CP

105. Step 3: Check your answer!
Not a lot to check…Just make sure you set up your equations correctly.
I double-checked it and I did it right…
12/29/2018
Geometry CP

106. Another type of solution
What do you notice about the graphs and equations?
y = -3x + 4
3x + y = 4
What do you think the solution, or point of intersection is?
12/29/2018
Geometry Honors

107. Infinitely Many Solutions
SAME LINE

108. Coinciding Lines (Infinitely Many Solutions)
These lines are the same!
Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS!
Coinciding lines have the same slope and y-intercepts.
12/29/2018
Geometry CP

109. Find the solution to the following system by the Graphing Method
Graph 6x + 4y = 12 and 3x + 2y = 6
12/29/2018
Geometry CP

110. JOURNAL: Does it have a solution?
Determine whether the following have one, none, or infinite
solutions by looking at the slope and y-intercept. Explain your reasoning. 1) 2)
y = 4 -1/2 x
y = 2x + 4
y = -6x + 8
y + 6x = 8 3)
y = -3/4x + 6
y = -3/4x - 6
12/29/2018
Geometry CP

111. Does it have a solution?
Determine whether the following have one, none, or infinite
solutions by just looking at the slope and y-intercepts. 1)
y = 4 -1/2 x
y = 2x + 4 2)
y = -6x + 8
y + 6x = 8 3)
y = -3/4x + 6
y = -3/4x - 6
ANS:
One Solution
ANS:
Infinite Solutions
ANS:
No Solution
12/29/2018
Geometry CP

112. What is the solution of the system graphed below?
(2, -2)
(-2, 2)
No solution
Infinitely many solutions
12/29/2018
Geometry CP

113. What is the solution of this system using the Graphing Method?
y = 2x - 2
y = 2x + 1
(2, -2)
(2, 1)
No solution
Infinitely many solutions
12/29/2018
Geometry CP

114. What is the solution of this system using the Graphing Method?
y = 2x - 2
y = 1/2x + 4
(4, 6)
(6, 4)
No solution
Infinitely many solutions
12/29/2018
Geometry CP

115. What is the solution of this system using the Graphing Method?
y = 3x - 8
(3, 1)
(4, 4)
No solution
Infinitely many solutions
12/29/2018
Geometry CP

116. What is the solution of this system using the Graphing Method?
y = 4x - 2
-4x + y = -2
(4, -2)
(-2, 4)
No solution
Infinitely many solutions
12/29/2018
Geometry CP

117. Solving a system of equations by the Graphing Method 
Let's summarize! There are 3 steps to solving a system using a graph.
Graph using slope and y – intercept. Be sure to use a ruler and graph paper!
Step 1: Graph both equations.
This is the solution! LABEL the solution (x, y)!
Step 2: Do the graphs intersect?
Substitute the x and y values into both equations to verify the point is a solution to both equations.
Step 3: Check your solution.
12/29/2018
Geometry CP

118. Include a graph and equations as examples.
Summarize Time
In your journals, write today’s date and the question below.
Describe systems of equations that have one solution, no solution, and infinitely many solutions?
Include a graph and equations as examples.
Answer the question in complete sentences with lots of details.
12/29/2018
Geometry CP

119. GRAPHING CALCULATOR Rewrite equation in y = form
Use the INTERSECT function to find the intersection point
12/29/2018
Geometry CP

120. 12/29/2018
Geometry CP

121. Your turn: GRAPHING EXAMPLES
y = - 3x and y = 2 – 4x
x + y = 1 and 2x + y = 4
3x + y = 1 and y = 8 +1/2x
2x + y = 1 and 5x + 4y = 10
y = 2x + 3 and y = x
6x + 4y = 12 and 3x + 2y = 6
12/29/2018
Geometry CP

122. GRAPHING CALCULATOR EXAMPLES
(2, - 6)
y = - 3x and y = 2 – 4x
x + y = 1 and 2x + y = 4
3x + y = 1 and y = 8 +1/2x
2x + y = 1 and 5x + 4y = 10
y = 2x + 3 and y = x
6x + 4y = 12 and 3x + 2y = 6
(3, -2)
(-2, 7)
(-2, 5)
No solution
Infinitely Many
12/29/2018
Geometry CP

123. “All I Do Is Solve” (Part I)
12/29/2018
Geometry CP

124. Check Your Understanding
Solve the system of equations using the Graphing Method. Check your solution.
y = 3x – 3
y = -x + 1
12/29/2018
Geometry CP

125. Group Self-Evaluation Form
Read each statement and rate your partner by circling one response for each statement.
12/29/2018
Geometry CP

126. Homework Assignment
Worksheet - Solve each system of equations by the Graphing Method.
12/29/2018
Geometry CP