How Many Solutions?
Solving Linear Equations
Writing Linear Equations
Graphs
Equivalent Equations
100
How many solutions does the equation have?
-2(x+3)=-2x-6
infinitely many
100
Solve:
4(2x-3)+4=8x-8
Infinitely Many Solutions
100
Twice the number decreased by 22 is 48. Create a linear equation to model this situation.
2x-22=24
100
Looking at the graph below, what does the point (5, 25) mean in this context?
5 books were sold for $25.
100
True or False:
The equation
(6x+12)=-3(6x+14) is equivalent to the equation (6x+12)/3=-3(6x+14)
False
200
x+5x+4=6x-3
No Solution
200
Solve:
5x-3=4(x+3)-2x
x=5
200
Write an equation to represent Olivia's cell phone plan.
y=30x+90
200
DAILY DOUBLE!
What does the slope of this graph mean in this situation?
200
True or False:
The equation (6x+12)/3=-18x-42 is equivalent to the equation (6x+12)/3=-3(6x+14)
True
300
How many solutions does the equation have?
3/2(2x+6)=3(x+2)
No Solution
300
Solve:
4(x-3)-(x-5)=0
x=7/3
300
A farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?
5 ducks 6 goats
300
What does the y-intercept mean in this context?
The weight of the jar with no marbles in it is 30 grams.
300
True or False: The equations -4x-2=6 and -32x-16=48 have the same solution.
True
400
How many solutions does this system have?
y=2x+5
y=2x-7
No Solutions
400
DAILY DOUBLE!
x=0
400
At Elisa's Printing Company LLC there are two kinds of printing presses: Model A which can print 70 books per day and Model B which can print 55 books per day. The company owns 14 total printing presses and this allows them to print 905 books per day. How many of each type of press do they have?
9 Model A
5 Model B
400
What does the y-intercept mean in this context?
There is a one-time fee of $150 to install a fence.
400
True or False: The equation 15x-5y=30 has the same solution as the equation 3x-y=-10 .
False
500
How many solutions does this system have?
3x+y=-2
6x-5y=10
One solution
500
Solve:
10-5x=3(x-4)-2(x+7)
x=6
500
Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks and how many spoons did they make last April?
7 forks and 20 spoons
500
What does the slope mean in this context?
It costs $15 more dollars for every additional foot of fencing that is installed.
500
A gym charges $30 per month plus a sign on fee of $150. If the equation t=30m+150 represents this situation, how many months did a person have this plan if they paid a total of t dollars? (hint: solve for m)!
m=(t-150)/30