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System ofEquations
Substitution Elimination Graphing
Q $100
Q $200
Q $300
Q $400
Q $500
Q $100 Q $100Q $100 Q $100
Q $200 Q $200 Q $200 Q $200
Q $300 Q $300 Q $300 Q $300
Q $400 Q $400 Q $400 Q $400
Q $500 Q $500 Q $500 Q $500
Final Jeopardy
JeopardyReal life scenarios
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What is the solution to this system of equations?
Jeopardy
3 3
7
y x
y x
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(1,6)
Jeopardy
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A system of equations has been graphed at the right. What is the solution to this system of equations?
Jeopardy
Each tick mark = 1
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(3, 3)
Jeopardy
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(1, 2) is a solution to which system of equations?
Jeopardy
4 2)
3
y xa
y x
1)
3
y xc
y x
4 4)
8 6
y xb
y x
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Jeopardy
1)
3
y xc
y x
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Given the system of equations, what do you know about their solution?
Jeopardy
3 2
6 2
y x
y x
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There is no solution.The lines have the same.The lines are parallel.They lines will not intersect.
Jeopardy
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Jeopardy
x y
-2 0
0 2
2 4
4 6
6 8
x y
-1 5
0 8
1 11
2 14
3 17
Each table represents a set of linear data. What is the solution to this system of equations?
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(-3, -1)
Jeopardy
x y
-4 -2
-3 -1
-2 0
0 2
2 4
4 6
6 8
x y
-3 -1
-1 5
0 8
1 11
2 14
3 17
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Solve this system of equations by substitution:
Jeopardy
3
14 4
d t
d t
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Jeopardy
(2, 6)
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Jeopardy
Solve this system of equations by substitution:
1.5
12 2.5
d t
d t
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Jeopardy
(3, 4.5)
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Jeopardy
Solve this system of equations by substitution:
232 8
y x
y x
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(6, 4)
Jeopardy
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Jeopardy
Solve this system of equations by substitution:
2 3
12
2
y x
y x
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(0, 2)
Jeopardy
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Which system of equations if already set up to use the substitution method to solve for the solution?
Jeopardy
3 4 12)2 3 8
x ya
x y
12
3)3
64
y xb
y x
3 1 12)3 3 12
x yc
x y
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Jeopardy
12
3)3
64
y xb
y x
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Jeopardy
You want to use the elimination method to solve for the solution to this system of equations.
3 7 8
5 8 6
x y
x y
Tell how you can eliminate the y term.
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Jeopardy
Multiply the first equation by -8 and the second equation by 7 and then add the equations.
Or
Multiply the first equation by 8 and the second equation by -7 and then add the equations
Or
Multiply the first equation by 8 and the second equation by 7 and then subtract the equations
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Jeopardy
Solve this system of equations by elimination:
60
20
y x
y x
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Jeopardy
(20, 40)
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Jeopardy
Solve this system of equations by elimination:
6 5 20
6 10 25
x y
x y
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Jeopardy
(-2.5, -1)
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Jeopardy
Solve this system of equations by elimination:
15
22 1 10
x y
x y
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Jeopardy
Infinitely many solutions because the two equations are the same line.
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Jeopardy
Solve this system of equations by elimination:
12
31 1
02 6
x y
x y
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(1, 3)
Jeopardy
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What best describes the systems of equations shown in the graph below?
Jeopardy
graphing
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Jeopardy
No Solution
graphing
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Which of the following is true for a system of equations to have an intersection at exactly one point?
a.) Both equations must have the same slope. b.) Both equations must have the same slope and the
same y-intercept. c.) The equations must have different slopes and the y-
intercepts can be the same or different.
Jeopardy
graphing
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Jeopardy
c.) The equations must have different slopes and the y-intercepts can be the same or different.
graphing
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What inequality statement is graphed at the right?
Jeopardy
graphing
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Jeopardy
11
2y x
graphing
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Jeopardy
The dark blue section represents the solution of a system of inequalities.
True or FalseThe points (4, 1) is in the solution set.
graphing
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Jeopardy
False
graphing
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Jeopardy
What inequality statement is graphed at the right?
graphing
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x < 2
Jeopardy
graphing
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Jeopardy
A buffet has one price for adults and another for children.The Taylor family has two adults and three children, and their bill was $40.50. The Wong family has three adults and one child. Their bill was $38. Write a system of equations to determine the price for an adult and for a child?
real life scenarios
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Jeopardy
2x + 3y = 40.50 3x + y = 38
real life scenarios
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Jeopardy
Suppose your community center sells a total of 292 tickets for a basketball game. An adult ticket costs $3 and a student ticket costs $1. The sponsors collect $470 in total ticket sales. Write a system of equations to determine how many adult and student tickets were sold?
real life scenarios
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Jeopardy
3a + s = 470 a + s = 292
real life scenarios
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Jeopardy
real life scenarios
Two health clubs offer different plans for physical training. Fit Zone charges a $30 initial fee and an additional $10 for each hour of physical training. Ultra Strength charges an initial fee of $55 and an additional $5 for each hour of physical training.
Bill buys 10 hours of physical training. Determine which health club plan would cost less for Bill.
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Jeopardy
real life scenarios
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Jeopardy
real life scenarios
Two health clubs offer different plans for physical training. Fit Zone charges a $30 initial fee and an additional $10 for each hour of physical training. Ultra Strength charges an initial fee of $55 and an additional $5 for each hour of physical training.
Identify the hours of physical training when both plans cost an equal amount.
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Jeopardy
real life scenarios
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Jeopardy
real life scenarios
Two health clubs offer different plans for physical training. Fit Zone charges a $30 initial fee and an additional $10 for each hour of physical training. Ultra Strength charges an initial fee of $55 and an additional $5 for each hour of physical training.
Describe which plan costs less with respect to hours of physical training.
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Jeopardy
real life scenarios
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Jeopardy
Complete the following statements:
1. A system of two linear equations has no solution if …2. A system of two linear equations has infinitely many solutions if …3. A system of two linear equations has exactly one solution if …
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1. The equations have different y-intercepts and the same slope (parallel lines)
2. The equations have the same y-intercept and the same slope (same lines)
3. The equations have different slopes and the same or different y-intercepts (intersecting lines)
Jeopardy