
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 11th, 2015, 03:14 PM  #1 
Senior Member Joined: Jan 2015 From: USA Posts: 107 Thanks: 2  Simultaneous very hard problem
Can someone help me solve this simultaneous equation? We are to find a and b so that the three equations have a solution in common. Thanx! 
June 11th, 2015, 04:48 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra 
By writing $a$ and $b$ in terms of $x$ using the first two equations, you can find an equation (or a pair of equations) that give three possible values of $x$. You can use these values in the first two equations to find $a$ and $b$. My solutions are $(a,b) \in \big\{(0,0), (3,4), (0,2)\big\}$ 
June 11th, 2015, 07:59 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
Adding the first and third equations gives 2x² + (b  2)x = 0, so x = 0 or 1  b/2. x = 0 implies a = b = 0. x = 1  b/2 implies 1  b + b²/4  3 + 3b/2  b = 0, i.e. (b  4)(b + 2)/4 = 0. It's easy to finish from there. 
June 13th, 2015, 08:15 PM  #4 
Senior Member Joined: May 2015 From: Varanasi Posts: 110 Thanks: 5 Math Focus: Calculus 
I dont see there is a very big problem in that, there are 3 unknowns and 3 equations though it will need some manipulation.You must write your attempt.

June 14th, 2015, 04:49 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  

Tags 
hard, problem, simultaneous 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Did I do this right? ( Hard problem)  yyttr4  Calculus  5  June 23rd, 2010 12:41 PM 
hard problem??  john mraz  Advanced Statistics  0  June 15th, 2010 12:32 AM 
simultaneous equations problem  sweetjane  Algebra  1  January 25th, 2010 09:10 PM 
simultaneous equation problem  manich44  Algebra  1  November 9th, 2009 08:59 AM 
Simultaneous Trig Problem/Lowest common multiple  zooloo45  Algebra  1  May 26th, 2009 09:24 AM 