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Question 24414: I am having trouble with this problem. I am to use the addition method and determine if the equations are independent, dependent or inconsistent.
x - y = 3
-6x + 6y + 17
same with this one
x + y + 13
22x + 36y = 356
Thanks for your help....
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE THE FOLLOWING EXAMPLE WHICH WILL HELP YOU.IF YOU STILL HAVE DIFFICULTY PLEASE COME BACK
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In the given system of equations is consistent and dependent, consistent and independent or inconsistent.
3x-y=7
6x-2x=9
what does these terms mean?
1 solutions
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Answer 12951 by venugopalramana(684) on 2006-01-13 01:20:47 (Show Source):
IS the given system of equations consistent
MEANS WHETHER THERE IS ANY SET OF VALUES FOR X AND Y WHICH SATISFIES BOTH THE GIVEN EQUATIONS.
and dependent,MEANS WHETHER ONE EQUATION CAN BE GOT FROM THE OTHER BY SUITABLE AND PERMISSIBLE TRANSFORMATION
consistent and independent,MEANS THAT ONE EQUATION CANNOT BE OBTAINED FROM THE OTHER EQUATION BY BY ANY SUITABLE AND PERMISSIBLE TRANSFORMATION .
or inconsistent.MEANS THERE ARE NO SET OF VALUES FOR X AND Y WHICH SATISFY BOTH THE EQUATIONS.
3x-y=7.....I.......
6x-2x=9...I THINK IT SHOULD BE 6X-2Y=9........II
what does these terms mean?NOW I THINK YOU KNOW WHAT THE TERMS MEAN.THERE ARE TESTS FOR FINDING THESE SITUATIONS.WE SHALL RESTRICT THE ANALYSIS TO YOUR PROBLEM AFTER THE CORRECTION MENTIONED ABOVE.
WE FIND THAT ON L.H.S OF THE 2 EQNS.WE HAVE 3X-Y AND 6X-2Y WHICH ARE DIRECT MULTIPLES BY 2 .THAT IS WE GET LHS OF EQN.2 BY MULTIPLYING THE EQN 1 WITH 2
WE GET EQN.I *2 ....6X-2Y=14
WHERE AS EQN.II SAYS 6X-2Y=9..SO IF WE TRY TO SATISFY EQN.I ,EQN II WILL NOT BE SATISFIED AND IF WE TRY TO SATISFY EQN II ,EQN.I WILL NOT BE SATISFIED.SO THERE ARE NO VALUES OF X AND Y WHICH SATISFY BOTH EQUATIONS.SO WE SAY THE GIVEN EQNS. ARE INCONSISTENT.
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