Systems of Equations Word Problems
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution1
Solving Systems of Linear Equations: Substitution2
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
If we were to do substitution and have a graph of the same system of equations would we get the same solution?
Yes.
Every equation graphs a specific line so no matter how you solve, you get the same solution!
(Graphs are definitely easier, but we don't always have graphed systems!)
100
Solve the systems of equations using substitution:
y=3x-10
x=2
(2,-4)
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 systems of equations to represent the situation.
y= 8x + 14
y= 7x + 16
200
What is the solution?
(-1,1)
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Isolate the variable
200
Solve the systems of equations using substitution:
y=2x-10
y=4x+8
(-9,-28)
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
What is your new (one) equation after performing substitution?
y=2x
3x+y=20
3x+(2x)=20 or
5x=20
300
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
300
How many solutions does the system of linear equations have?
y = (-5/3)x + 3
y = (1/3)x - 3
One
400
Mr. Galosh, the owner of two car dealerships in Morristown, is holding a contest to see which one can sell the most cars. Morristown Cars has already sold 10 car, and Galosh Auto has sold 12 cars. Going forward, the salespeople at Morristown Cars think they can sell 3 cars per day, whereas the salespeople at Galosh Auto are aiming for sales of 1 car per day. Write a systems of equations to represent the situation.
y= 3x + 10
y= x + 12
400
Solve the systems of linear equations by graphing:
400
How would you isolate x in this equation?
6y+x=20
subtract 6y from both sides to get:
x=20-6y
400
Solve the systems of equations using substitution:
2x - y = 6
x = y + 5
(1, -4)
400
How many solutions does the system of linear equations have?
y = 3x + 9
2y = 6x + 18
Infinitely many solutions
500
How do we write solutions to systems of linear equations?
(x,y)
500
Solve this by graphing:
2x - y = 4
x + 3y = 3
(3,2)
500
Use the substitution method to solve the system of linear equations:
y=2x
3x+y=20
Solution: (4,8)
500
Use the substitution method to solve the system of linear equations:
6x + 2y = 10
y = -3x -4
No solution
500
How many solutions does the system of linear equations have?
y = 2x - 5
4y = 8x - 5
Zero or None