Graphing
Substitution
Elimination
Application
Mystery!
100
What is the solution to a system containing two lines that do not intersect?
No solution
100
DOUBLE POINTS: You need to make sure you have at least one equation in ____________ before you can solve a system using substitution.
slope-intercept form
y=mx+b
y=
100
Which variable would eliminate?
x
100
Write two equations to represent the following situations:
One burger (b) and two sodas (s) costs $8.50.
3 burgers (b) and one soda (s) costs $12.00.
b + 2s = 8.50
3b + s = 12.00
100
How many solutions does this system of equations contain?
Infinite solutions
200
Explain how you would graph the line:
y = -4x + 3
Plot a point at (0,3), then go down 4 and over 1
200
How would you set up to solve this problem if you wanted to use substitution?
-5x+6(5/6x+2)=12
200
What could you multiply the second equation by to be able to eliminate one of the variables?
1) -3 to eliminate the x
2) 2 to eliminate the y
200
DOUBLE POINTS: At Starbucks, 1 bagel and 1 coffee costs $9.00. 3 bagels and 2 coffees costs $25.50. How much does one bagel cost?
$7.50
200
What does the solution to a system of equations represent?
The point of intersection of the two equations.
300
Sketch the graph y = 2/3x + 1 on your whiteboard.
300
Use substitution to solve the system of equations.
No solution
300
What would your first step be if you wanted to solve this system using elimination?
1) Multiply the first equation by 5
2) Multiply the second equation by 2
300
At Old Navy, 3 shirts cost $15.75. At Old Navy, 3 shirts and one pair of jeans costs $43.00. How much do 2 pairs of jeans cost?
$65 - $32.50 per pair of jeans.
300
If two equations had the same slope and different y-intercepts, how many solutions would there be?
No solution - they would be parallel lines
400
DOUBLE POINTS: How many solutions does this system of equations have?
1 - it's not no solution because they are not parallel lines - they will intersect at some point.
400
Use substitution to solve the system of equations. 
(-8, 16)
400
Use elimination to solve this system of equations.
(6, 3)
400
Ms. Otis has no money in her bank account. She saves $475 per week. Mrs. Tichy has $1,000 in her bank account. She saves $225 per week. After how many weeks will Ms. Otis and Mrs. Tichy have the same amount of money?
4 weeks
400
Write the following equation in slope-intercept form:
6x - y = 2
y = 6x - 2
500
Write the following equation in slope-intercept form:
3x - 6y = -12
y = 1/2x + 2
500
Use substitution to solve the system of equations.
(8, -2)
500
1) Explain when it might be beneficial to use graphing over the other methods.
2) Explain when it might be beneficial to use elimination over other methods.
1) Graphing is very visual; it would be the preferred method if both equations were in slope-intercept form and/or when the numbers are small, whole numbers.
2) Elimination would be the preferred method when both equations are in standard-form and/or when you can easily eliminate a variable.
500
Mr. Keegan is looking for a new cellphone plan. He is choosing between Verizon and AT&T. Verizon charges $45 per month plus $8.25 per GB used. AT&T charges $35 per month plus $6.99 per GB used. Mr. Keegan uses roughly 5 GB per month. Which plan would be cheaper for him?
AT&T
500
Explain what the lines y = 2 and x = -5 look like.