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 November 16th, 2007, 11:22 AM #1 Newbie   Joined: Sep 2007 Posts: 17 Thanks: 0 Subsitution or Elimination x+4y-3z=-8 3x-y+3z=12 x+y+6z=1 November 16th, 2007, 01:22 PM #2 Senior Member   Joined: Oct 2007 From: France Posts: 121 Thanks: 1 As you like it. November 17th, 2007, 06:32 AM #3 Senior Member   Joined: Dec 2006 Posts: 1,111 Thanks: 0 Try using a matrix on your calculator. It's faster. November 17th, 2007, 10:27 AM   #4
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Quote:
 Originally Posted by Infinity Try using a matrix on your calculator. It's faster.
It's been a while, but I think you can find the answer on a TI-83 with

rref([[1,4,-3,8][3,-1,3,12][1,1,6,1]]) November 17th, 2007, 07:49 PM #5 Global Moderator   Joined: Dec 2006 Posts: 21,134 Thanks: 2341 x + 4y - 3z = -8 * * * *[A] 3x - y + 3z = 12 * * * [B] x + y + 6z =1 * * * * * [C] [A] + 3[B] - [C] gives 9x = 27, so x = 3. [B] + [C] gives 4x + 9z = 13, so z = (13 - 4x)/9 = (13 - 12)/9 = 1/9. From [C], y = 1 - x - 6z = 1 - 3 - 2/3 = -2 2/3. November 18th, 2007, 02:59 AM #6 Senior Member   Joined: Oct 2007 From: France Posts: 121 Thanks: 1 x + 4y - 3z = -8 [A] 3x - y + 3z = 12 [B] x + y + 6z =1 [C] [A]+[B] gives 4x+3y=4 [D] 2[A]+[C] gives 3x+9y=-15, or x+3y=-5 [E] [D]-[E] gives 3x=9 , so x=3 [D] gives 3y=4-4x=-8, so y=-8/3 [A] gives 3z=x+4y+8=4-32/3+8=11-32/3=1/3, so z=1/9 November 19th, 2007, 06:33 PM #7 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 x + 4y - 3z = -8 [A] 3x - y + 3z = 12 [B] x + y + 6z =1 [C] [B] + [C] gives 4x + 9z = 13 or (13 - 4x) / (9) = z [D] 2[A] + [C] gives 3x + 9y = -15 or x + 3y = -5 or (-x - 5) / (3) = y [E] [A] gives x + 4((-x - 5) / (3)) - 3((13 - 4x) / (9)) = x - (4/3)(x) - 20/3 - 13/3 + (4/3)(x) = x - 11 = -8 or x = 11 - 8 = 3 [D] gives z = (13 - (4)(3)) / (9) = 1/9 [E] gives y = (-3 - 5) / (3) = -8/3 Tags elimination, subsitution Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post lightful Linear Algebra 1 May 13th, 2012 02:06 PM TJ44 Algebra 3 March 29th, 2012 09:46 AM ewuc Algebra 2 September 17th, 2011 01:59 PM MRKhal Algebra 2 April 2nd, 2011 02:17 AM shepherdm1270 Calculus 1 April 14th, 2008 11:51 AM

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