Graphing
Solve the system by graphing.
y = 2x + 5
y = 1/2 x - 1
(-4, -3)
Solve the system by elimination.
x + y = 3
x - y = 1
(2, 1)
Solve the system by substitution.
y = -4
8x - 3y = 20
(1, -4)
Tickets for your school's play are $3 for students and $5 for non-students. On opening night, 937 tickets are sold and $3943 is collected.
Write a system of equations to represent this situation.
Let x = the number of student tickets
Let y = the number of non-student tickets
x + y = 937
3x + 5y = 3943
Find if the system has one solution, no solution, or infinitely many solutions.
y = 2x + 5
y = 2x - 7
No solution
Solve the system by graphing.
y = x + 4
y = 4
(4,0).
Solve the system by elimination.
x - y = 12
3x + y = 4
(4, -8)
Solve the system by substitution.
-5x + y = 15
5x = 15 - 2y
(-1, 10)
Tickets for your school's play is $2 for students and $4 for non-students. On opening night, 290 tickets were sold and $844 is collected. Write and solve a system of equations to find how many tickets were sold to students.
Let x = the number of student tickets
Let y = the number of non-student tickets
x + y = 290
2x + 4y = 844
158 tickets were sold to students.
Find if the system has one solution, no solution, or infinitely many solutions.
12x + 3y = 16
-36x - 9y = 32
No solution
Solve the system by graphing.
y = 2/3x + 2
y = 2x - 5
(-3,-4)
Solve the system by elimination.
4x - y = 20
x + y = 5
(5,0)
Solve the system by substitution.
y = 5x - 7
-3x - 2y = -12
(2,3)
The basketball concession stand sells cheese pizza for $2 per slice and pepperoni pizza for $3 per slice. The concession stand sells a total of 82 slices of pizza and makes $200. Write and solve a system of equations to find how many of each type of pizza was sold.
Let x = the number of cheese pizza slices
Let y = the number of pepperoni pizza slices
x + y = 82
2x + 3y = 200
There were 46 slices of cheese pizza and 36 slices of pepperoni pizza sold.
Find if the system has one solution, no solution, or infinitely many solutions.
-9x + 6y = 0
-12x + 8y = 0
Infinitely many solutions
Solve the system by graphing.
6x = 2y + 2
x = 2
(2,3)
Solve the system by elimination.
-x + 2y = 15
x + 3y = 15
(-3, 6)
Solve the system by substitution.
-4x + y = 6
-5x - y = 21
(-3,-6)
You are on the Student Council decorating committee and are in charge of buying balloons. You want to use both latex and mylar balloons. The latex balloons cost $0.10 each and the mylar balloons cost $0.50 each. You need 125 balloons and you have $32.50 to spend. Write and solve a system of equations to find how many of each type of balloon you can buy.
Let x = the number of latex balloons
Let y = the number of mylar balloons
x + y = 125
0.1x + 0.5y = 32.50
You can buy 75 latex balloons and 50 mylar balloons.
Find if the system has one solution, no solution, or infinitely many solutions.
4y = -4x + 4
y = -1/2x - 3
One solution (8, -7)
Solve the system by graphing.
2x + y = 4
y = x - 5
(3, -2)
Solve the system by elimination.
2x - y = -8
2x + y = 8
(0,8)
Solve the system by substitution.
-5x + y = -3
3x - 8y = 24
(0,-3)
You are on the Student Council decorating committee and are in charge of buying balloons. You want to use both latex and mylar balloons. The latex balloons cost $0.15 each and the mylar balloons cost $0.60 each. You need 100 balloons and you have $42.00 to spend. Write and solve a system of equations to find how many of each balloon you can buy.
Let x = the number of latex balloons
Let y = the number of mylar balloons
x + y = 100
0.15x + 0.6y = 42
You can buy 40 latex balloons and 60 mylar balloons.
Find if the system has one solution, no solution, or infinitely many solutions.
y = x + 4
y = -4/3x - 3
One solution (-3,1)