Solving by Graphing
Solve the following by Graphing:
y = – 1/3 x + 4 y = 4/3 x – 1
The answer is: (3,3)
Solve using substitution
2x – y = 9
x = –y + 3
Solution is (4,-1)
Solve using Elimination:
4x – 9y = -21
4x + 3y = -9
Solution is (-3,1)
McDonalds sells one customer 4 Big Macs and 3 orders of fries for $22. Another customer ordered 5 Big Macs and 6 orders of fries for $32.
Write the system that represents this situation.
4b+3f=22
5b+6f=32
Solve the following by graphing:
x + 2y = 10
y = 2x+5
The answer is (5,0)
Solve using Substitution:
6x – y = 2
x + 2y = –17
Solution is (-1,-8)
Solve Using Elimination:
2x + 3y = 12
6x + 4y = 26
The solution is (3,2)
An aquarium charges one price for adults and another price for children. Two groups visit the aquarium.
The first group has 4 adults and 20 children, and they paid a total of $320 for admission. The second group has 4 adults and 23 children, and they paid a total of $356.
Write a system of equations for the situation.
4a+20c=320
4a+23c=356
Solve by graphing:
y=2x+8
-2x+y=3
The solution is No Solution, as the lines are parallel.
Solve using substitution:
4y=1
8x-4y=3
Solution is (0.5,0.25)
Solve Using Elimination:
2x – 7y = -12
-2x + 7y = 9
No Solution as the lines are parallel.
Lydia has 10 coins in her pocket, made up of dimes and quarters. The value of her coins is $1.45. How many dimes and how many quarters does Lydia have?
7 dimes and 3 quarters.
Solve the following:
y=x+4
2y-2x=8
The solution is infinite as these are the same line.
Solve Using Substitution:
-3x+y=12
6x-2y=18
No Solution is these lines are parallel.
Solve Using Elimination:
-2x+3y=16
3x+4y=-7
The solution is (-5,2)
Two companies charge different amounts for the use of their dance halls. Party Time Charges a $100 flat fee plus $50 per hour. Let’s Dance Company charges a $175 flat fee plus $25 per hour.
For what number of hours do the two companies change the same amount?
At 3 hours.