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6.1 Solving Systems Of Equations By Graphing Bell Work Evaluate each expression for x = 1 and y = –3. 1. x – 4y 2. –2x + y Write each expression in slope-intercept form. 3. y – x = 1 4. 2x + 3y = 6 5. Cheetah Vs. Usain Bolt Video: http://youtu.be/U6K-F9Bjl8s D i s t a n c e 100 m (5.95, 100) Bolt= (9.58, 100) Cheetah = Time 9 10 D i s t a n c e Bolt= 100 m (9.58, 100) Cheetah = 40 m Time 9 10 Solving Linear Equations By Graphing • Our goal is to; 1. Graph TWO lines on same graph 2. Locate where they intersect (or if they do at all) Solving a Linear Equation • Linear equations can look like; y = 3x + 7 Or -3x + y = 7 Or 7 + 3x = y Or … 3 Graphing Possibilities 1. Intersecting Lines 2. Parallel Lines 3. Coinciding Lines 1) Intersecting Lines • The point where the lines intersect is your solution. • The solution of this graph is (1, 2) (1,2) What is the solution of the system graphed below? 1. 2. 3. 4. (2, -2) (-2, 2) No solution Infinitely many solutions Where do these graphs intersect 2) Parallel Lines • These lines never intersect! • Since the lines never cross, there is NO SOLUTION! • Parallel lines = SAME SLOPE, different y-int. 2 Slope = = 2 1 y-intercept = 2 y-intercept = -1 Parallel Lines Hi, I’m Two Our Slopes Must Be Twins!!! Hey, I’m Two Too! What is the solution of this system? y = 3x + 3 y = 3x - 12 1. 2. 3. 4. (3, -12) Parallel solutions No solution Infinitely many solutions 3) Coinciding Lines • These lines are the same! • Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! • Coinciding lines = SAME SLOPE, SAME Y-INT. 2 Slope = = 2 1 y-intercept = -1 What is the solution of this system? y = 3x - 8 y = 3x - 8 1. 2. 3. 4. (3, 1) (4, 4) No solution Infinitely many solutions Lets try one: Find the solution to the following system: y = -2x+4 y = x -2 m=-2 b=4 m=1 b=-2 Step 1:Graph both equations Step 2: Find Where the lines intersect? THE SOLUTION: (2,0) You try: Where do the lines intersect? y = 2x – 1 y = –x + 5 Graph both equations Where do they intersect? The point is (2, 3) Try again: Find the solution to the system Graph both equations Where do they intersect? NO SOLUTION Find the Solution Summary • Intersecting Lines have how many solutions? • Parallel Lines have the same what? • How can you tell if two equations are coinciding without graphing them? • Do you have to graph the system to know the answer if both equations have the same slope? HOMEWORK • Find an example in real life (just like Usain Bolt vs. Cheetah) and graph it. – I want to see the following 1. 2. 3. 4. What two things are you graphing What is your x-axis and y-axis Graph them Do they intersect? Where?