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Warm UpI can solve systems of equations
by substitution
1. Graph 2. Solve: 3. Write a system of equations:Sara has 16 baseball cards and buys 7 more each week. Ted has 2 baseball cards and collects 9 more each week. Write a systems of equations and solve to find out when they will have the same number of cards.
Warm UpI can solve systems of equations
by substitution
1. Graph
Warm UpI can solve systems of equations
by substitution
Solve:
Warm UpI can solve systems of equations
by substitution
Write a system of equations:Sara has 16 baseball cards and buys 7 more each week. Ted has 2 baseball cards and collects 9 more each week. Write a systems of equations and solve to find out when they will have the same number of cards.
Homework Questions
-8
xy
x y
x + y
Diamond Problems
4
-42
3
xy
x y
x + y
Diamond Problems
-14
-11
-4
12
xy
x y
x + y
Diamond Problems
16-64
Solve the following system using any method
Solve by Graphing
The solution isn’t at a clear point!
What else could we try?
Try it!
• Try problems 1 and 2 on your practice sheet using the method we just discovered. See if you can solve the systems
Solving Systems with Substitution
Steps
1. Determine variable to substitution
2. Make substitution 3. Solve
Example:
**Substitute in for y
Solving Systems with SubstitutionSteps
4. Plug back into an original equation
5. Solve for missing variable
6. Write answer as a point
Example:
Practice
20 minutesCheck your answers on
the back table
Writing and Solving Systems
April sold 75 tickets to a school play and collected a total of $495. If the adult tickets cost $8 each and child tickets cost $5 each, how many adult tickets and how many child tickets did she sell?
Define variables:
System of equations:
State your solution(s):
Solve April sold 75 tickets to a school play and collected a total of $495. If the adult tickets cost $8 each and child tickets cost $5 each, how many adult tickets and how many child tickets did she sell?
a = the number of adult tickets.c = the number of child tickets.
a + c = 758a + 5c = 495
There were 40 adult tickets and 35 child tickets sold.
40 + 35 = 758(40) + 5(35) = 495
320 + 175 = 495
a + c = 758a + 5c = 495
a = 75 – c
8(75 – c) + 5c = 495600 – 8c + 5c = 495
600 - 3c = 495105 = 3c35 = c
a + c = 75a + 35 = 75
a = 40
Writing and Solving Systems
At a baseball game, Jose bought four hot dogs and one soda for $12. At the same time, Allison bought two hot dogs and four sodas for $13. Find the cost of one hot dog and one soda.
Define variables:
System of equations:
State your solution(s):
Solve At a baseball game, Jose bought four hot dogs and one soda for $12. At the same time, Allison bought two hot dogs and four sodas for $13. Find the cost of one hot dog and one soda.
h = the price of hot dog.s = the price of a soda.
4h + s = 122h + 4s = 13
A hot dog costs $2.50 and a soda costs $2.00.
4(2.5) + 2 = 122(2.5) + 4(2) = 13
5 + 8 = 13
4h + s = 122h + 4s = 13
s = 12 – 4h
2h + 4(12 – 4h) = 132h + 48 – 16h = 13
48 – 14h = 1335 = 14h2.5 = h
4h + s = 124(2.5) + s = 12
10 + s = 12s = 2
TextbookHomework
