1. Warm-Up Pocono Ski Resort offers skiing lessons for $70 per hour and a $15 registration fee. Write an equation that models the total cost, y, of a lesson that is x hours long. Then, graph the equation. Blue Mountain offers lessons for $89 per hour with no registration fee. Could we create an equation of this situation with the same variables?

2. 6-1 Solving Systems by Graphing

3. What is a SYSTEM? We can model this situation using 2 linear equations. A __________ is a set of two or more equations with related unknowns Denoted by a brace Two or more linear equations form a __________. Any ordered pair that makes all of the equations in a system is a of a system of linear equations. SYSTEM SOLUTION TRUE SYSTEM

4. SOLVE by Graphing Step 2: Find Intersection Point.. Step 1: Graph each equation It appears to be at (-2,0). Step 3: Check solutions in both equations.

5. SOLVE by Graphing Can you find any intersection points? Why or why not? Step 1: Graph each equation These lines are parallel. Therefore, there is no solution to this system.

6. SOLVE by Graphing How many solutions does this system have? Step 1: Graph each equation INFINITELY MANY

7. Conclusions Systems of linear equations can have: solution, solutions or many solutions. If a system has no solution, the lines are _____________. These lines will have the same ________ but different. If a system has infinitely many solutions, the lines have the same ________ and. Systems that have ________ solution consist of lines that have slopes. ONE NO INFINITELY PARALLEL SLOPEY-INTERCEPTS SLOPES ONE DIFFERENT

8. Example Suppose one puppy weighs 5 pounds at birth and grows at a rate of.25 pound per month over the first several months. Another puppy weighs 4 pounds at birth and grows at a rate of.5 pound per month. Write a system of linear equations to model the weight of the puppy, y, after x months. After 4 months, the puppies will weigh 6 pounds 4 5

9. Check your solution:

10. Example A plant nursery is growing a tree that is 3 feet tall and grows at an average rate of 1 ft per year. Another tree at the nursery is 4 feet tall and grows at an average rate of.5 ft per year. After how many years will the trees be the same height? The trees will both be 5 feet after 2 years.

11. Check your solution: Homework: Sect. 6.1 p. 385-387 #’s 10-32 even