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**Unformatted text preview: **Gaussian Elimination - two lines case 1-14-13-12-11-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 10 Gaussian Elimination - two lines case 2-4-3-2-1 1 2 3 4 5 6 7 8-2-1 1 2 3 4 5 6 Gaussian Elimination - two lines case 3-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 10-6-5-4-3-2-1 1 2 3 4 5 6 Gaussian Elimination - two lines Three Cases y = m 1 x + b 1 (1) y = m 2 x + b 2 (2) Three cases: 1 Case I: one solution m 1 6 = m 2 , slopes different cross at one point. 2 Case II: no solution m 1 = m 2 , slopes same parallel lines. b 1 6 = b 2 y-intercepts not same no common points. 3 Case III: infinite number of solutions. Must find all of them. m 1 = m 2 , slopes same parallel lines. b 1 = b 2 y-intercepts are same all points common to both lines. all points common to both lines are solutions. Gauss-Jordan Elimination Case I: one solution 2x + 3y = 8 (3) 6x- 2y = 2 (4) Gauss-Jordan Elimination 2 3 8 6- 2 2-- R2- > 1 2 R2 2 3 8 3- 1 1-- R 2 R 2 + (- 1) R 1 2 3 8 1- 4- 7 R 1 R 2-- 1- 4- 7 2 3 8-- R 2 R 2 + (- 2) R 1 Gauss-Jordan Elimination...

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