1. 6-1 Solving Systems by Graphing AGAIN Goals: Interpret solutions for special problems. Model a real-life problem using a linear system. Eligible Content: A1.1.2.2.1 / A1.1.2.2.2

2. Special Problems No solution – the two lines are parallel so there is no point of intersection. Many solutions – the two equations create the same line so they intersect everywhere along the line.

3. Solve the system by graphing: y = 2x + 3 -2x + y = -2 y = 2x + 3 m = 2 b = 3 -2x + y = -2 +2x y = 2x – 2 m = 2 b = -2 There is no solution

4. Solve the system by graphing: y = -3x + 8 6x + 2y = 16 y = -3x + 8 m = -3 b = 8 6x + 2y = 16 -6x 2y = -6x + 16 2 2 2 y = -3x + 8 m = -3 b = 8 There are many solutions

5. Examples Solve each system by graphing (not all problems are special!!) 1. 2x + y = 5 2x + y = 1 no solution 2. 3x + y = 7 4x – 2y = 6 (2, 1) 3. 6x + y = -5 -12x – 2y = 10 many solutions

6. A.(0, 0) B.no solution C.infinitely many D.(1, 3) Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

7. Practice 1. 3x + y = 4 -9x – 3y = 12 2. 4x + 2y = 8 y = -2x + 4 No solution Many solutions

8. Word Problems Slope is the rate of change y-intercept is the beginning amount If the numbers are too big you might have to use a calculator to graph!

9. Word Problem #1 You are growing two different trees. The first tree is 4 foot tall and is growing at a rate of 1 foot per year. The second tree is 2 foot tall and is growing at a rate of 1.5 feet per year. How long until the two trees are the same height? y = 1x + 4 y = 1.5x + 2 4 years

10. Word Problem #2 A math club’s website has 200 daily visits and is increasing at a rate of 50 visits per month. A science club’s website has 400 daily visits and is increasing at a rate of 25 visits per month. How many months until the two websites have the same amount of visits? y = 50x + 200 y = 25x + 400 8 months

11. Word Problem #3 Two car rental agencies have different rates. At the first agency there is a charge of $25 plus $.50 per mile. At the second agency there is a charge of $40 plus $.25 per mile. How many miles will you drive for the two agencies to be the same price? y =.50x + 25 y =.25x + 40 60 miles

12. A.225 weeks B.7 weeks C.5 weeks D.20 weeks Alex and Amber are both saving money for a summer vacation. Alex has already saved $100 and plans to save $25 per week until the trip. Amber has $75 and plans to save $30 per week. In how many weeks will Alex and Amber have the same amount of money?

13. Homework Pages 338-339 #16-24 even #9, 25, 26 (graphs on calculator)