SOLUTION: What is a coinciding equation?

Question 24714: What is a coinciding equation?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
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'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

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