Systems of Equations Word Problems
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution
Solving Systems of Linear Equations: Elimination
How Many Solutions?
100
The Town Recreation Department rents out their batting cage. During the summer, it costs $5 to rent a bat and $7 per hour to use the batting cage. During the winter, it costs $3 to rent a bat and $4 per hour to use the batting cage. Write a systems of equations to represent the situation.
y= 7x + 5
y= 4x + 3
100
14) What is the solution to the system of linear equations?
(2,2)
100
What is your new (one) equation after performing substitution?
y=2x
3x+y=20
3x+(2x)=20 or
5x=20
100
What two operations (+, -, *, /) can you do to cancel out a variable to make it "disappear"?
Addition and subtraction!
100
How many solutions does the system of linear equations have?
One! (-4,-6)
200
On the windowsill is a plant that is 14 centimeters tall. It is growing 8 centimeters per week. A second plant, which is 16 centimeters tall, is on the coffee table. It is growing 7 centimeters per week. Write a system of equations to represent the situation.
y= 8x + 14
y= 7x + 16
200
What is the solution?
(-1,1)
200
How would you isolate x in this equation?
6y+x=20
subtract 6y from both sides to get:
x=20-6y
200
If adding two linear equations does not cancel out a variable to make it "disappear", what else can you do?
Subtract!
200
How many solutions does the system of linear equations have?
y = 3x - 5
y = 3x + 7
Zero or None
300
Kelly and Sallie both went bowling last weekend, but not together. Kelly went during open bowling time, paying $3 for shoe rental and $6 per hour. Sally went on family night, when each hour was $4 and shoe rental was $1. Write a systems of equations to represent the situation.
y= 6x + 3
y= 4x +1
300
Solve Using Graphing:
y = 5/3x + 2
y = -3
300
Use the substitution method to solve the system of linear equations:
y=2x
3x+y=20
Solution: (4,8)
300
Solve the systems of equations using the elimination method:
5x-4y=4
-5x+6y=14
(8, 9)
300
How many solutions does the system of linear equations have?
y = (-5/3)x + 3
y = (1/3)x - 3
One
400
Amy and Jen played laser tag at two different places. Amy was charged 
fee and a 
for each game. Jen was charged 
fee and a 
for each game. If Amy and Jen paid the same amount to play, how many games did they each play? How much did they pay?
3 games for $50!
400
Solve the systems of linear equations by graphing:
400
Using the substitution method, solve the system of linear equations.
y=-4x+18
y=-6
(6, -6)
400
Solve the systems of equations using the elimination method:
10x+3y=-20
x+3y=-2
(-2, 0)
400
How many solutions does the system of linear equations have?
y = 3x + 9
2y = 6x + 18
Infinitely many solutions
500
Steve and Sara each improved their yard by planting rose bushes and ivy pots. Steve spent 
on 
and 
. Sara spent 
on 
and 
. What is the cost of one rose bush and one ivy pot?
9 rose bushes and 5 ivy pots.
500
Solve this by any method(graphing, substitution, elimination):
2x - y = 4
x + 3y = 3
(3,2)
500
Using the substitution method, solve the system of linear equations:
-5x+3y=-12
y=5x-14
(3, 1)
500
Use the elimination method to solve the system of linear equations:
10x+y=7
-10x-y=-14
No solution
500
How many solutions does the system of linear equations have?
y = 2x - 5
4y = 8x - 5
Zero or None