Systems - Number of Solutions
Systems - Graphing
Systems - Solving Using Substitution
Systems - Harder Solving Using Substitution
Scatter Plots
100
Identify if the following system has no solution, one solution, or infinitely many solutions WITHOUT SOLVING.
{(x,+,y,=,7),(2x,+,2y,=,14):}
Infinitely Many Solutions.
(You can see that the second equation is just double the first equation)
100
How many solutions does the following system of equations have?
No Solutions.
The lines will never intersect.
100
Solve the system of equations.
{(y=x+3),(y=3x-3):}
(3,6)
100
Solve the system of equations.
{(2x,+,3y,=,16),(y,=,2x,-,8):}
(5,2)
100
Would this relationship show a positive or negative association:
Pounds of apples you buy and amount of money you spend on apples
Positive Association
As pounds of apples increases, the amount of money you spend increases (they both increase together)
200
Identify if the following system has no solution, one solution, or infinitely many solutions WITHOUT SOLVING.
{(x,+,y,=,4),(x,+,y,=,8):}
No Solutions.
(The same two numbers can't add to both 4 and 8)
200
How many solutions does the following system of equations have?
One Solution.
The lines intersect at one point. The solution would be (2,0).
200
Solve the system of equations.
{(y=x-5),(y=2x-16):}
(11,6)
200
Solve the system of equations.
{(3x,+,2y,=,22),(y,=,-1/3x,+,4):}
(6,2)
200
Would this relationship show a positive or negative association:
Speed of a car and the amount of time it takes for the car to get to its destination
Negative Association
As the speed of the car increases, the amount of time it takes to get to its destination decreases (as one increases the other decreases)
300
Identify if the following system has no solution, one solution, or infinitely many solutions WITHOUT SOLVING.
{(y=4x+3),(y=-4x+5):}
One Solution.
(Since the equations have different slopes, the lines will intersect at one point)
300
Here is a graph for one of the equations in a system of two equations. The solution to the system is (5,3). Could the other equation in the system be:
y=2x-7
Yes. Fill in (5,3) into the equation. Remember that 5 is the x-value and 3 is the y-value so:
3=2(5)-7
300
Solve the system of equations.
{(y=x-6),(y=3x-14):}
(4,-2)
300
Solve the system of equations.
{(2x,+,3y,=,25),(y,=,-1/2x,+,8):}
(2,7)
300
Does the following scatter plot show a positive or negative association?
Positive 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.
{(2x,+,4y,=,8),(6x,+,12y,=,24):}
Infinitely Many Solutions.
(You can see that the second equation is just three times the first equation)
400
Here is a graph for one of the equations in a system of two equations. The solution to the system is (3,-3). Could the other equation in the system be:
y=-1/3x-2
Yes. Fill in (3,-3) into the equation. Remember that 3 is the x-value and -3 is the y-value so:
-3=-1/3(3)-2
400
Tyler buys apples and oranges at the store. Apples cost $2 a pound and oranges cost $4 a pound. If Tyler spends $20 on apples and oranges, complete this table showing some possible combinations of each type purchased.
400
Solve the system of equations.
{(3x,+,y,=,9),(y,=,5x,-,7):}
(2,3)
400
Does the following scatter plot show a linear or not linear association?
Not Linear.
It looks more like a curved line than a straight line.
500
Identify if the following system has no solution, one solution, or infinitely many solutions WITHOUT SOLVING.
{(2x,+,2y,=,6),(2x,+,2y,=,-2):}
No Solutions.
(Notice that the left side of the equations are the same, but 6 does not equal -2)
500
Here is a graph for one of the equations in a system of two equations. The solution to the system is (7,9). Could the other equation in the system be:
y=4x-2
No. Fill in (7,9) into the equation. Remember that 7 is the x-value and 9 is the y-value so: (notice this equation is not true)
9=4(7)-2
500
Tyler buys apples and oranges at the store. Apples cost $2 a pound and oranges cost $4 a pound. If Tyler spends $20 on apples and oranges, write an equation to represent this situation using x for pounds of apples and y for pounds of oranges.
2x+4y=20
500
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 x for pounds of apples and y for pounds of oranges.
Tyler buys 2 pounds of apples and 4 pounds of oranges.
{(2x,+,4y,=,20),(y,=,x,+,2):}
(2,4)
500
What vocabulary word describes the "Here I Am" point?
Outlier