My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
November 16th, 2007, 10:22 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
titans4ever0927 is offline  
 
November 16th, 2007, 12:22 PM   #2
Senior Member
 
Joined: Oct 2007
From: France

Posts: 121
Thanks: 1

As you like it.
Richard André-Jeannin is offline  
November 17th, 2007, 05:32 AM   #3
Senior Member
 
Joined: Dec 2006

Posts: 1,111
Thanks: 0

Try using a matrix on your calculator. It's faster.
Infinity is offline  
November 17th, 2007, 09:27 AM   #4
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
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]])
CRGreathouse is offline  
November 17th, 2007, 06:49 PM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 20,831
Thanks: 2161

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.
skipjack is offline  
November 18th, 2007, 01:59 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
Richard André-Jeannin is offline  
November 19th, 2007, 05:33 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
johnny is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
elimination, subsitution



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Roots of Polynomials via subsitution with uneven powers lightful Linear Algebra 1 May 13th, 2012 01:06 PM
Elimination Techniques TJ44 Algebra 3 March 29th, 2012 08:46 AM
Gaussian elimination ewuc Algebra 2 September 17th, 2011 12:59 PM
Elimination Techniques MRKhal Algebra 2 April 2nd, 2011 01:17 AM
subsitution to find the following indefinite integrals shepherdm1270 Calculus 1 April 14th, 2008 10:51 AM





Copyright © 2019 My Math Forum. All rights reserved.