<PRE><B>Question 26347</B>
SEE THE FOLLOWING TO GET AN IDEA OF THE TOPIC.IF STILL IN DIFFICULTY PLEASE CONTACT ME AND I SHALL HELP FURTHER
AS REGARDS GRAPHING GIVE DIFFERENT VALUES TO X AND FIND Y FROM THE GIVEN RELATION .SEE BELOW
I EQN....X+Y=4
X.............0.........1...........2...........3..............4........ETC...
Y=4-X.........4.........3...........2...........1..............0.........ETC
II EQN.....5X+Y=8
X...........0...........1............2.............3......ETC.........
Y=8-5X......8...........3............-2............-7.....ETC...........
THE GRAPHS WILL LOOK LIKE THIS.

 {{{ graph( 500, 500, -10, 10, -10, 10, 4-x,8-5x )}}}
THE 2 LINES INTERSECT AT X=1 AND Y=3 WHICH IS THE UNIQUE SOLUTION TO THESE EQNS.THAT IS THEY ARE CONSISTENT AND INDEPENDENT.IF THEY ARE DEPENDENT YOU WILL GET ONE IDENTICAL LINE FOR BOTH EQNS.THAT IS THEY HAVE INFINITE SOLUTIONS ON THAT LINE. IF THEY ARE INCONSISTENT YOU WILL GET 2 PARALLEL LINES WHICH DO NOT INTERSECT AND HENCE THERE IS NO SOLUTION
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What is a coinciding equation?
1 solutions

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Answer 13848 by venugopalramana(791)   on 2006-01-28 11:16:56 (Show Source): 

consider these 2 eqns 
x+y=2...........i
2x+2y=4.........ii
if the first eqn is given to us ,the second one can be derived by us by multiplying the first eqn. with 2 on either side. so the second eqn.does not give us any additional information ,but is a derivative or dependent eqn. of eqn.i.read the following for additional related information.in case of more than 2 or for that matter any number of equations , if one or more of them could be sinilarly derived by a suitable combination of other eqns.,then we say they or dependent eqns.
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When using gaussian elimination, can an inconsistant solution have a general solution? i worked out the matrix and came to a spot where 1=-3 and 1=10.4 (inconsistant 1 can&#39;t equal 2 different solutions); would there still be a way to formulate a general solution such as x=(2-4x,2-3x,x,0) = (2,2,0,0) + x(-4,-3,1,0)
I hope this is enough information to clearly explain my question. thanks
I THINK YOU ARE CONFUSED BETWEEN ...INCONSISTENT,AND DEPENDENT EQUATIONS.
AS THE NAME IMPLIES AN INCONSISTENT SET OF EQUATIONS HAS NO SOLUTION AS THEY ARE INCONSISTENT.FOR EXAMPLE 
X+Y=2
2X+2Y=3....HENCE THERE IS NO QUESTION OF GETTING A GENERAL SOLUTION FOR THAT BY ANY METHOD GAUSSIAN ELIMINATION OR ANY..
CONSISTENT AND DEPENDENT EQNS.HAVE INFINITE SOLUTIONS GIVEN BY A GENERAL FORMULA AS YOU HAVE MENTIONED..FOR EX.
X+Y=1
2X+2Y=2....THE GERAL FORMULA IS Y=1-X...OR (X,1-X)IS A SOLUTION SET..LIKE (1,0),(2,-1) ETC....
FINALLY CONSISTENT AND INDEPENDENT EQNS.HAVE UNIQUE SOLUTION..FOR EXAMPLE
X+Y=2
X-Y=0...HAVE ONE UNIQUE SOLUTION X=1 AND Y=1
NOW YOU CAN USE GAUSSIAN ELIMINATION TO THE 3 EXAMPLES ABOVE AND SEE WHAT YOU GET.IF YOU STILL AVE DIFFICULTY COME BACK </PRE>