Math 11 Opener - 11/16/11
Learning Target: Solve Systems by Substitution
Solve the following system by substitution:
2x + 3y = 6
x = -8 - 2y
1
Homework Key: Substitution WS #1
x=3
y=6
x=1
y=1
x=2
y = -2
x=2
y = -3
x = -4
y=6
x=7
y = 21
x=1
y=2
x = -1
y=1
2
x = -5
y = -3
infinite
solutions
1x + 30 = 2.50x
20 rides
3
Notes:
Solving Systems by Substitution cont...
Sometimes a system won't have a variable by
itself. You will have to get the variable alone
first, then you can use substitution.
Example:
Solve using substitution.
2x + 5y = 7
x + 4y = 2
HINT: Look for the
variable that is
almost by itself!
Example:
4x + y = -2
3x + 2y = 11
4
What are the types of solutions a system can have?
You can see these types of solutions algebraically
through substitution:
6x - 2y = 5
-3x + y = 7
-2x + y = -5
6x - 3y = 15
Summary:
No solution will end up as:
Infinite solutions will end up as:
5
Exit Ticket:
Do this in your notes!
Solve the following system using substitution.
4x + 8y = 8
x + 2y = 6
6