Lesson: Number of Solutions
Presentation
•
Mathematics
•
9th Grade
•
Medium
Standards-aligned
Christopher Gassler
Used 54+ times
FREE Resource
8 Slides • 8 Questions
1
Multiple Choice
YES I have my notebook out
No, I know it means a bad grade
2
Number of Solutions
Objective: Determine the number of solutions to linear equations.
3
Math Response
WARMUP - Solve: -5x - 13 = 15 - 3x
4
WARMUP EXPLAINED
-5x - 13 = 15 - 3x
+3x
+3x
-2x - 13 = 15
+13
+13
-2x = 28
-2
-2
x = -14
-5(-14) - 13 = 15 - 3(-14)
Plug in -14
70 - 13 = 15 + 42
57 = 57
There is ONE SOLUTION to this equation...-14
5
EXAMPLE
(No Solution)
2x + 3 = 2x + 7
6
Multiple Select
What qualities are associated with "no solution" problems?
(choose ALL that apply)
There are an infinite number of solutions.
The variables all cancel and only constants are left.
The final equation is ALWAYS TRUE.
The final equation is ALWAYS FALSE.
There is only one solution for the equation.
7
EXAMPLE
(Infinite Solutions)
2x + 6 = 2(x + 3)
(Identity)
(All Real Numbers)
8
Multiple Select
What qualities are associated with "identity" problems?
(choose ALL that apply)
There are an infinite number of solutions.
The variables all cancel and only constants are left.
The final equation is ALWAYS TRUE.
The final equation is ALWAYS FALSE.
There is only one solution for the equation.
9
"NO SOLUTION" and "IDENTITY" are often confused with equations with a solution of zero
10
11
Categorize
16 + 6x = 2(3x + 8)
15 = 7 - 3x
2 + 4x - 12 = 4(x - 3)
12
EXAMPLE
Given the equation: 7(x - p) = -42 + 7x
For what value of p does the equation have infinite solutions?
A) 42
B) 6
C) -6
D) 7
13
Multiple Choice
Given the equation:
4(x - p) = -32 + 4x
For what value of p does the equation have infinite solutions?
8
32
16
4
14
EXAMPLE
Given the equation: px - 12 + 4x = 6x - 16
For what value of p does the equation have no solutions?
A) -4
B) 2
C) 6
D) -6
15
Multiple Choice
Given the equation:
14x - 12 = 3x + 5 + px
For what value of p does the equation have no solution?
11
14
12
1
16
Fill in the Blanks
Type answer...
YES I have my notebook out
No, I know it means a bad grade
Show answer
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MULTIPLE CHOICE
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