
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 26th, 2013, 10:42 AM  #1 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0  Simultaneous Equations
Hi, I've been trying to solve these simultaneous equations, but I just can't. Any help would be greatly appreciated. x + y + z = 5 1/x + 1/y + 1/z = 1/5 xy + xz + yz = 9 
February 26th, 2013, 11:42 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,782 Thanks: 607  Re: Simultaneous Equations
Solution a bit long...go enter x+y+z+1/x+1/y+1/z+x*y+x*z+y*z+19/5 = 0 here: http://www.numberempire.com/equationsolver.php Perhaps time to quit? 
February 26th, 2013, 12:41 PM  #3 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0  Re: Simultaneous Equations
Thanks for the reply, but that website just gives me the solutions. I'm actually just interested in the method used to solve.

February 26th, 2013, 12:43 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,441 Thanks: 872 Math Focus: Elementary mathematics and beyond  Re: Simultaneous Equations
Are x, y and z integers? Or are they real numbers? Rational numbers, perhaps?

February 26th, 2013, 02:06 PM  #5 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0  Re: Simultaneous Equations
The solutions are integers. By inspection, I can see that the solutions are 3, 3, and 5, but that doesn't tell me which value corresponds to each variable, which is why I'm looking for an algebraic method for solving.

February 26th, 2013, 02:10 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 16,791 Thanks: 1238 
Multiplying the second equation by xyz gives xy + xz + yz = xyz/5, so xyz = 45. From the third equation, xyz + xz² + yz² = 9z, so 9z = 45 + z²(5  z). Hence z³  5z²  9z + 45 = 0, which factorizes as (z + 3)(z  3)(z  5) = 0. It's easy to finish from there. 
February 26th, 2013, 02:21 PM  #7 
Newbie Joined: Feb 2013 Posts: 16 Thanks: 0  Re: Simultaneous Equations
Thank you!!


Tags 
equations, simultaneous 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
simultaneous log equations  dralay  Algebra  3  July 25th, 2013 02:47 AM 
Simultaneous Equations  bilano99  Algebra  3  June 30th, 2012 05:48 AM 
Simultaneous Equations  poochie03  Algebra  2  November 6th, 2011 04:35 AM 
Simultaneous equations  MathematicallyObtuse  Algebra  1  November 29th, 2010 06:08 AM 
simultaneous equations anyone?  empiricus  Algebra  4  August 30th, 2009 04:28 AM 