Systems - Number of Solutions
Systems - Story Problems
Systems - Solving Using Substitution
Systems - Harder Solving Using Substitution
Scatter Plots
100
Write a system of equations for the graph below. Identify if the following system has no solution, one solution, or infinitely many solutions.
{(y=4+2x),(y=-5+2x):}
What is no solutions because the lines have the same slope and are parallel?
100
To join a dancing club, there is a $30 startup fee and a $15 monthly fee. To join a soccer club, there is a $50 startup fee and a $10 monthly fee. Write and solve a system of equations to determine after how many months they will have the same cost.
What is they will both cost $90 after 4 months?
{(y=30+15x),(y=50+10x):}
(4,90)
100
Solve the system of equations.
{(y=x+3),(y=3x-3):}
What is (3,6)?
100
Solve the system of equations.
{(2x,+,3y,=,16),(y,=,2x,-,8):}
What is (5,2)?
100
The scatter plot shows that the longer students studied, the higher their exam scores. What is the slope of the linear model? What does the slope represent in this context?
What is 5? This tells us that the score on the final exam increases by 5 for every hour spent studying.
200
Identify if the following system has no solution, one solution, or infinitely many solutions.
What is infinite solutions, because they are the same line?
200
The water level of a lake is 38 feet, and it is dropping at a rate of 1.5 feet per day. The water level of a pond is 20 feet, and is rising by 3 feet per day. Write and solve a system of equations to determine when the lake and pond will have the same water level.
What is they will both have a water level of 32 feet after 4 days?
{(y=38-1.5x),(y=20+3x):}
(4,32)
200
Solve the system of equations.
{(y=x-5),(y=2x-16):}
What is (11,6)?
200
Solve the system of equations.
{(3x,+,2y,=,22),(y,=,-1/3x,+,4):}
(6,2)
200
The scatter plot shows that the longer students studied, the higher their exam scores. What score does the model predict for a student who spends 5 hours studying?
What is about 75?
300
Use the graph to determine the solution to the system of equations.
What is (-1,1), because that is where they intersect?
300
Tyler buys apples and oranges at the store. Apples cost $2 a pound and oranges cost $4 a pound. Tyler spends $20 on apples and oranges together. Tyler buys 2 more pounds of oranges than apples. Write and solve a system of equations to represent this situation using a for pounds of apples and o for pounds of oranges.
What is Tyler buys 2 pounds of apples and 4 pounds of oranges?
{(2a,+,4o,=,20),(o,=,a,+,2):}
300
Solve the system of equations.
{(y=x-6),(y=3x-14):}
What is (4,-2)?
300
Solve the system of equations.
{(2x,+,3y,=,25),(y,=,-1/2x,+,8):}
What is (2,7)?
300
Does the following scatter plot show a positive or negative association? Is the association linear or non-linear?
What is a positive linear association?
The line of best fit would have a positive slope.
400
Identify if the following system has no solution, one solution, or infinitely many solutions WITHOUT SOLVING.
{(y=2x+3),(y=3+2x):}
What is infinitely many solutions because the equations have the same slope and vertical intercept?
400
A ski rental service charges a $5 flat rate for the initial rental and an additional $ 3 per hour. A snowboard rental service charges an $8 flat rate for the initial rental and an additional $2 per hour. Write and solve a system of equations to find out when the ski rental and snowboard rental will have the same cost.
What is they will both cost $14 after 3 hours?
{(y=5+3x),(y=8+2x):}
(3,14)
400
Solve the system of equations.
{(y=3x+5),(y=-2x-3):}
What is (-1.6,0.2)?
400
Solve the system of equations.
{(3x,+,y,=,9),(y,=,5x,-,7):}
What is (2,3)?
400
The scatter plot shows an association between the miles a town is East of a lake and the inches of snowfall received. What does the point (30,35) represent in this context?
What is a location that is 30 miles East of the lake that got 35 inches of snowfall?
500
Identify if the following system has no solution, one solution, or infinitely many solutions WITHOUT SOLVING.
{(y=3x),(y=3x-1):}
What is no solutions because the equations have the same slope?
500
The graph shows the total cost to ride the Blue Cab and the Yellow Cab. What is the solution to the system and what does the solution mean in this context?
What is (3,8)? After 3 miles, they both cost $8.
500
Solve the system of equations.
{(y=-3-5x),(y=-2x-12):}
What is (3,-18)?
500
Solve the system of equations.
{(y=2x-1),(2x+3y=-7):}
What is (-1/2, -2)?
500
What vocabulary word describes the "Here I Am" point?
What is an outlier?