1. Warm-Up
Tickets for a concert cost $10 each if you order them online, but you must pay an $8 service charge per order. The tickets are $12 each if you buy them at the door on the night of the concert.
Write a system of equations to model the situation. Let y be the total cost. Let x be the number of tickets purchased.

2. 6.2: Solving Systems Algebraically

3. Substitution method
You can solve linear systems by solving one of the equations for one of the ______________.
Then, ______________ the expression for that variable into the other equation. This is called the ________________________.
When a system has at least one equation that can be easily __________ , for a variable, the system can be solved efficiently using substitution.
VARIABLES
SUBSTITUTE
SUBSTITUTION METHOD
SOLVED

4. Example: What is the solution to the system
STEP 1: Substitute 5x for y in the second equation.
STEP 2: Solve the equation for x.
STEP 3: Replace x and solve for y in the first equation.
x = 2
y = 10
STEP 4: Solution to the system:

5. Solving for a Variable and Using Substitution:
Example: What is the solution to the system
STEP 1: Rewrite one of the equations so a variable is by itself.
STEP 2: Substitute this value into the other equation.
STEP 3: Solve for the variable.
STEP 4: Replace in the first equation.
x = 2
y = 4
STEP 5: Solution to the system:

6. Special Systems IDENTITY
If you get an like 5 = 5 when solving a system this means there are an infinite number of solutions to the system. If you get a statement like 0 = -2 then there are no solutions to the system.
FALSE

7. Infinitely Many Solutions
Examples
1) How many solutions does each system have?
Infinitely Many Solutions
No Solution

8. Homework: Sect. 6.2 p. 393-395 #’s 12-24 even