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How Many Solutions
Graphing
Substitution
Elimination
100
How many solutions does the following system have? y=3x - 4 and y=3x - 2
Zero Solutions
100
Solve the following system by graphing: y= 4x + 3 and y= -x - 2
(-1, -1)
100
Solve the following system by substitution. y=6x - 11 and -2x - 3y= -7
(2,1)
100
Solve the following system by elimination. -4x + 4y = -8 and 4x - 6y = 16
(-2, -4)
200
How many solutions does the following system have? y=4x - 7 and y=3x + 4
One Solution
200
Solve the following system by graphing: y= 2x - 6 and y = 2x + 3
No Solution
200
Solve the following system by substitution. 2x− 3y= −1 and y=x− 1
(4, 3)
200
Solve the following system by elimination. -12x - 15y = -9 and 4x +5y = 3
Infinitely many solutions
300
How many solutions does the following system have? 2x + y = 3 and -4x - 2y = -6
Infinitely Many Solutions
300
Solve the following system by graphing: y = 1/3x - 3 and y = -x +1
(3,-2)
300
Solve the following system by substitution. y = -3x + 5 and 5x - 4y = -3
(1,2)
300
Solve the following system by elimination. -3x + 2y = 17 and x - 5y = -10
(-5, 1)
400
How many solutions does the following system have? y = 4x + 14 and y = -4x + 14
One Solution
400
Jennifer, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of $10 plus $1 per pound. The second charges $5 plus $2 per pound. Jennifer determines that, given her package's weight, the two courier services are equivalent in terms of cost. How much will it cost?
$15
400
Sheela, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of $15 plus $5 per kilogram. The second charges $7 plus $6 per kilogram. Sheela determines that, given her package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?
The package will weigh 8 kilograms and cost $55.
400
Solve the following system by elimination. 4x + 6y = 22 and -2x +4y = 10
(1,3)
500
All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7 students each and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles total?
8 vans and 7 buses
500
Bobby just got his commercial driver's license and is starting a new career as a truck driver. Getting trained and licensed involved a one-time cost of $500. Gas and insurance end up costing him $4 per mile. For his first delivery, Bobby will get paid $400 plus $5 per mile that he drives. If he drives a certain distance on this delivery, Bobby will break even, making back all the money he had to spend. How much would both the costs and the earnings be?
$900
500
The volleyball team and the wrestling team at Millersburg High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $1 per car. In addition, they have already brought in $90 from past fundraisers. The wrestling team has raised $21 in the past, and they are making $4 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. How many cars will that take? What will that total be?
After washing 23 cars, both teams will have raised $113.
500
The difference of two numbers is 3. Their sum is 13. Find the numbers.
5 and 8