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.

6.2: Solving Systems Algebraically

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

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:

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:

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

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

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