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8-1 Solve Systems by Graphing 9P9: Solve 2X2 systems graphically

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Possible outcomes of 2 lines 1)They cross (intersect) in one place: 1 solution 2)They do not cross (Parallel): No Solution 3)They coincide (same equation): infinite number of solutions

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Why? If you want to compare to cell phone plans based on (minutes, Cost). AT&T Verizon What does the point where they cross represent? Minutes and cost are the same Which charges less per minute? Verizon, line not as steep How much does AT&T charge for activation? $0

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Example 1: Is (1,2) solution to this system? for y = x+1 & 2x + y = 4 2 = (1) + 2 = 4 2=2 yes2 + 2 =4 4 = 4 yes So (1,2) is a solution to this system

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Example 2: Is (-3,2) solution to the system? a + b = -1 & b + 3a = = (-3) =4 -1 = -1yes 2 + (-9) = 4 -7 = 4 no So (-3,2) is not a solution to this system

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Ex 3: Find Solution by graphing Hint: Find point(s) of intersection x + y = 3 and x – y = 1 -x y = -x y x -1 = y The solution is (2,1)

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Ex 4: y – 2x = 3 & y = 2x x y = 3 + 2x Hey when they have the same slopes they are parallel and don’t cross. That means there is no solution!!

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Ex 5: 3y - 2x = 6 & +2x +2x 3y = 6 + 2x Hey, these are the same line so all the points are the same or infinite # of solutions

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Find solutions by graphing Ex 6: x + 2y =7 & x = y + 4 Remember to solve for y! -x 2y = 7- x x - 4 = y The solution is (5,1)

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Assignment 8-1/ /8-28 even,32, 40-46

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