# Week 8 - Section 8.1 2x y 4 x 0 2(0) y 4 y (1) 4(1) y 4 (0,...

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Section 8.1

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2 4 0 2(0) 4 ( 1) 4( 1) 4 (0, 4) 0 2 0 4 2 4 2 4 2 2 2 (2,0) 2 6 0 2(0) 6 ( 1) 6( 1) 6 (0, 6) 0 2 0 6 2 6 2 6 2 2 3 (3,0) x y x y y y y x x x x x y x y y y y x x x x - = = - = - - = - = - - = - = = = = - = = - = - - = - = - - = - = = = =
-8 -6 -4 -2 2 4 6 8 -8 -6 -4 -2 2 4 6 8 x y Since the lines are parallel, then there is no solution. Inconsistent system

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x-2y=8 x=0 0-2y=8 -2y=8 -2y 8 -2 2 4 (0, 4) 0 2(0) 8 8 (8,0) 3 2 12 0 3(0) 2 12 2 12 2 12 2 2 6 (0, 6) 0 3 2(0) 12 3 12 3 12 3 3 4 (4,0) y y x x x y x y y y y y x x x x = - = - - = - = = - = = - = - = - = - - = - - = - = = = =
-8 -6 -4 -2 2 4 6 8 -8 -6 -4 -2 2 4 6 8 x y The lines intersect at (2,-3), therefore the solution to the system is (2,-3)

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3 6 9 0 3(0) 6 9 6 9 6 9 6 6 3 2 3 (0, ) 2 0 3 6(0) 9 3 9 3 9 3 3 3 (3,0) x y x y y y y y x x x x - = = - = - = - = - - = - - = - = = = = 2 3 0 0 2 3 2 3 2 3 2 2 3 2 3 (0, ) 2 0 2(0) 3 3 (3,0) x y x y y y y y x x - = = - = - = - = - - = - - = - = =
-8 -6 -4 -2 2 4 6 8 -8 -6 -4 -2 2 4 6 8 x y Since the two equations have the same graph, then the system has infinitely many solutions. Dependent System

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(-3,4) 5(-3)+7(4)=b -15+28=b b=13 mx+y=22 m(-3)+4=22 -3m+4-4=22-4 -3m=18 -3m 18 -3 3 6 m = - = - Section 8.2
2x + 3y = 1 (Equation 1) 5x+3y = 16

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## This note was uploaded on 04/04/2009 for the course MATH Math/116 taught by Professor Jamespierce during the Fall '08 term at University of Phoenix.

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Week 8 - Section 8.1 2x y 4 x 0 2(0) y 4 y (1) 4(1) y 4 (0,...

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