One-Step /Two-Step Equations
Multi-Step Equations
No Solution / Same Solution / Infinite Solutions
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More Equations
100
4 = -8 + x
x= 12
100
Which of the systems of equations has a solution of (4, 3)?
y=x−1 y=2x+1 x+y=6 x−y=1
y=−x+7 y=x+3 y=2x y=−2x+3
A
y=x−1
y=−x+7
100
Two equations have the same slope and the same y-intercept. What does this tell us about the system?
What is infinitely many solutions?
y=2x+4
2y=4x+8
100
Which functions are nonlinear? Select three such functions.
A, C, E
100
Solving Equations
4x + 3 = 7
x = 1
200
6x – 13 = 11
x= 4
200
5 + 3c = 11 + c
A. c = 3
B. c = 4
C. c = 5
D. c = 6
A. c = 3
200
How do you determine if a system of equations has one solution without doing one of the 3 methods?
Compare the slopes and y-intercepts of the equations.
If the slopes are different, the lines will intersect once, meaning the system has one solution.
y=2x+1
y=−x+4
200
Two tanks hold water. Tank A starts with 120 gallons and gains 8 gallons each hour. Tank B starts with 300 gallons and loses 12 gallons each hour.
Write an equation for each tank that represents the amount of water after x hours.
A = 120 + 8x
B = 300 − 12x
200
Triangles 5
Hearts 3
300
3 = -2 – x
x= -5
300
Look at the equations below. Identify which equations has no solutions.
A.
7x − 4 = 5x + 10
B.
12 − 3x = −3(x+4)
C.
4x + 8 = 2(2x+5)
D.
9 − x = 2x + 9
Answer: B and C
300
Mason didnt multiply 1/4 and -12
Correct Answer
x=72
300
Write a system of equation for the scenerio and explain how you would solve.
x + 3y = 97
2x + 2y = 94
Substitution
Graphing
Elimination
400
5x = -80
x= -16
400
Solving Equations
14 = (3a + 6) + 2
a=2
400
Two equations have the same slope but different y-intercepts. What does this tell us about the system?
What would the graph look like?
y=3x+2
y=3x−5
The lines would be parallel.
400
k=−16
400
(multiple choice)
Heart = 6
500
x/2 + 5 =10
x= 10
500
Solving Equations
-21 = 7(5k - 8)
k = 1
500
Select all the equations that have no solution.
A. 4(x − 2) = 4x + 10
B. 3x + 7 = 3x − 1
C. 5(x + 1) = 5x + 5
D. 2x − 3 = x + 4
A (gives −8 = 10 → no solution)
B (gives 7 = −1 → no solution)
500
The equation
d=4t+6
is used to represent the distance d (in meters) of a robot after t seconds.
What is the value of t if the robot has traveled 38 meters?
A. 4 seconds
B. 6 seconds
C. 8 seconds
D. 10 seconds
C. 8 seconds
500
x/3 - 6 = -3
x= 9