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
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
Marko1011 is offline  
 
February 26th, 2013, 11:42 AM   #2
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 9,467
Thanks: 640

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?
Denis is offline  
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.
Marko1011 is offline  
February 26th, 2013, 12:43 PM   #4
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,492
Thanks: 889

Math Focus: Elementary mathematics and beyond
Re: Simultaneous Equations

Are x, y and z integers? Or are they real numbers? Rational numbers, perhaps?
greg1313 is online now  
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.
Marko1011 is offline  
February 26th, 2013, 02:10 PM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 17,221
Thanks: 1294

Multiplying the second equation by xyz gives xy + xz + yz = xyz/5, so xyz = -45.
From the third equation, xyz + xz + yz = -9z, so -9z = -45 + z(5 - z).
Hence z - 5z - 9z + 45 = 0, which factorizes as (z + 3)(z - 3)(z - 5) = 0.
It's easy to finish from there.
skipjack is offline  
February 26th, 2013, 02:21 PM   #7
Newbie
 
Joined: Feb 2013

Posts: 16
Thanks: 0

Re: Simultaneous Equations

Thank you!!
Marko1011 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

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





Copyright © 2017 My Math Forum. All rights reserved.