document.write( "Question 44737This question is from textbook College Algebra
\n" ); document.write( ": Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.\r
\n" ); document.write( "\n" ); document.write( "2y = 1 - 4x
\n" ); document.write( "2x + y = 0 \n" ); document.write( "
Algebra.Com's Answer #29610 by venugopalramana(3286)\"\" \"About 
You can put this solution on YOUR website!
SEE THE FOLLOWING AND TRY
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\n" ); document.write( "SEE
\n" ); document.write( "\solve each of the follwing systems by substitution.
\n" ); document.write( "5x-2y=-5............I
\n" ); document.write( "y-5x=3......................II...Y=3+5X..........PUT IN EQN.I
\n" ); document.write( "5X-2(3+5X)=-5
\n" ); document.write( "5X-6-10X=-5
\n" ); document.write( "-5X=6-5=1
\n" ); document.write( "X=-1/5
\n" ); document.write( "Y=3+5X=3+5*(-1/5)=3-1=2
\n" ); document.write( "THESE ARE CONSISTENT INDEPENDENT EQNS.AND HENCE HAVE A UNIQUE SOLUTUIN NAMELY...
\n" ); document.write( "=-1/5 AND Y=2THE FOLLOWING AND TRY\r
\n" ); document.write( "\n" ); document.write( "Equations/44050: solve each of the following systems by graphing
\n" ); document.write( "3x-6y=9
\n" ); document.write( "x-2y=3
\n" ); document.write( "1 solutions
\n" ); document.write( "Answer 28988 by venugopalramana(2194) About Me on 2006-06-28 00:45:24 (Show Source):
\n" ); document.write( "You can put this solution on YOUR website!
\n" ); document.write( "SEE THE FOLLOWING AND TRY
\n" ); document.write( "solve each of the following systems by sustitution.
\n" ); document.write( "8x-4y=16....................I
\n" ); document.write( "y=2x-4....................II....PUT THIS IN EQN.I
\n" ); document.write( "8X-4(2X-4)=16
\n" ); document.write( "8X-8X+16=16
\n" ); document.write( "16=16.....OK...
\n" ); document.write( "HENCE THE EQNS.ARE DEPENDENT ANE THERE ARE INFINITE SETS OF SOLUTIONS..ANY SET WITH
\n" ); document.write( "X=ANY VALUE......SAY'0'
\n" ); document.write( "AND Y=2X-4=2*0-4=-4 IS A SOLUTION SET.
\n" ); document.write( "YOU CAN GIVE ANY VALUE TO X,FIND CORRESPONDING Y AND THAT IS THE SOLUTION SET.\r
\n" ); document.write( "\n" ); document.write( "Equations/44051: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
\n" ); document.write( "2x+3y=1
\n" ); document.write( "5x+3y=16
\n" ); document.write( "1 solutions
\n" ); document.write( "Answer 28987 by venugopalramana(2194) About Me on 2006-06-28 00:44:02 (Show Source):
\n" ); document.write( "You can put this solution on YOUR website!
\n" ); document.write( "SEE THE FOLLOWING AND TRY
\n" ); document.write( "-------------------------------
\n" ); document.write( "solve each of the follwing systems by substitution.
\n" ); document.write( "5x-2y=-5............I
\n" ); document.write( "y-5x=3......................II...Y=3+5X..........PUT IN EQN.I
\n" ); document.write( "5X-2(3+5X)=-5
\n" ); document.write( "5X-6-10X=-5
\n" ); document.write( "-5X=6-5=1
\n" ); document.write( "X=-1/5
\n" ); document.write( "Y=3+5X=3+5*(-1/5)=3-1=2
\n" ); document.write( "THESE ARE CONSISTENT INDEPENDENT EQNS.AND HENCE HAVE A UNIQUE SOLUTUIN NAMELY...
\n" ); document.write( "=-1/5 AND Y=2\r
\n" ); document.write( "\n" ); document.write( "Equations/44052: slove each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
\n" ); document.write( "x+5y=10
\n" ); document.write( "-2x-10y=-20
\n" ); document.write( "1 solutions
\n" ); document.write( "Answer 28986 by venugopalramana(2194) About Me on 2006-06-28 00:42:35 (Show Source):
\n" ); document.write( "You can put this solution on YOUR website!
\n" ); document.write( "SEE THE FOLLOWING AND TRY
\n" ); document.write( "-----------------------------
\n" ); document.write( "solve each of the following systems by sustitution.
\n" ); document.write( "8x-4y=16....................I
\n" ); document.write( "y=2x-4....................II....PUT THIS IN EQN.I
\n" ); document.write( "8X-4(2X-4)=16
\n" ); document.write( "8X-8X+16=16
\n" ); document.write( "16=16.....OK...
\n" ); document.write( "HENCE THE EQNS.ARE DEPENDENT ANE THERE ARE INFINITE SETS OF SOLUTIONS..ANY SET WITH
\n" ); document.write( "X=ANY VALUE......SAY'0'
\n" ); document.write( "AND Y=2X-4=2*0-4=-4 IS A SOLUTION SET.
\n" ); document.write( "YOU CAN GIVE ANY VALUE TO X,FIND CORRESPONDING Y AND THAT IS THE SOLUTION SET.\r
\n" ); document.write( "\n" ); document.write( "Equations/44055: solve each of the follwing systems by substitution.
\n" ); document.write( "5x-2y=-5
\n" ); document.write( "y-5x=3
\n" ); document.write( "1 solutions
\n" ); document.write( "Answer 28985 by venugopalramana(2194) About Me on 2006-06-28 00:39:28 (Show Source):
\n" ); document.write( "You can put this solution on YOUR website!
\n" ); document.write( "solve each of the follwing systems by substitution.
\n" ); document.write( "5x-2y=-5............I
\n" ); document.write( "y-5x=3......................II...Y=3+5X..........PUT IN EQN.I
\n" ); document.write( "5X-2(3+5X)=-5
\n" ); document.write( "5X-6-10X=-5
\n" ); document.write( "-5X=6-5=1
\n" ); document.write( "X=-1/5
\n" ); document.write( "Y=3+5X=3+5*(-1/5)=3-1=2
\n" ); document.write( "THESE ARE CONSISTENT INDEPENDENT EQNS.AND HENCE HAVE A UNIQUE SOLUTUIN NAMELY...
\n" ); document.write( "=-1/5 AND Y=2\r
\n" ); document.write( "\n" ); document.write( "Equations/44056: solve each of the following systems by sustitution.
\n" ); document.write( "8x-4y=16
\n" ); document.write( "y=2x-4
\n" ); document.write( "1 solutions
\n" ); document.write( "Answer 28984 by venugopalramana(2194) About Me on 2006-06-28 00:35:11 (Show Source):
\n" ); document.write( "You can put this solution on YOUR website!
\n" ); document.write( "solve each of the following systems by sustitution.
\n" ); document.write( "8x-4y=16....................I
\n" ); document.write( "y=2x-4....................II....PUT THIS IN EQN.I
\n" ); document.write( "8X-4(2X-4)=16
\n" ); document.write( "8X-8X+16=16
\n" ); document.write( "16=16.....OK...
\n" ); document.write( "HENCE THE EQNS.ARE DEPENDENT ANE THERE ARE INFINITE SETS OF SOLUTIONS..ANY SET WITH
\n" ); document.write( "X=ANY VALUE......SAY'0'
\n" ); document.write( "AND Y=2X-4=2*0-4=-4 IS A SOLUTION SET.
\n" ); document.write( "YOU CAN GIVE ANY VALUE TO X,FIND CORRESPONDING Y AND THAT IS THE SOLUTION SET.\r
\n" ); document.write( "\n" ); document.write( "Equations/44057: solve each of the following systmes by substitution.
\n" ); document.write( "4x-12y=5
\n" ); document.write( "-x+3y=-1
\n" ); document.write( "1 solutions
\n" ); document.write( "Answer 28983 by venugopalramana(2194) About Me on 2006-06-28 00:31:42 (Show Source):
\n" ); document.write( "You can put this solution on YOUR website!
\n" ); document.write( "solve each of the following systmes by substitution.
\n" ); document.write( "4x-12y=5................I
\n" ); document.write( "-x+3y=-1...............II.....X=3Y+1..PUT THIS IN EQN.I
\n" ); document.write( "4(3Y+1)-12Y=5
\n" ); document.write( "12Y+4-12Y=5
\n" ); document.write( "4=5...NOT POSSIBLE
\n" ); document.write( "HENCE EQNS. ARE INCONSISTENT AND THERE IS NO SOLUTION\r
\n" ); document.write( "\n" ); document.write( "Equations/44059: solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent.
\n" ); document.write( "10x+2y=7
\n" ); document.write( "y=-5x+3
\n" ); document.write( "1 solutions
\n" ); document.write( "Answer 28982 by venugopalramana(2194) About Me on 2006-06-28 00:22:33 (Show Source):
\n" ); document.write( "You can put this solution on YOUR website!
\n" ); document.write( "SEE THE FOLLOWING AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK
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\n" ); document.write( "IS the given system of equations consistent
\n" ); document.write( "MEANS WHETHER THERE IS ANY SET OF VALUES FOR X AND Y
\n" ); document.write( "WHICH SATISFIES BOTH THE GIVEN EQUATIONS.
\n" ); document.write( "and dependent,MEANS WHETHER ONE EQUATION CAN BE GOT
\n" ); document.write( "FROM THE OTHER BY SUITABLE AND PERMISSIBLE
\n" ); document.write( "TRANSFORMATION
\n" ); document.write( "consistent and independent,MEANS THAT ONE EQUATION
\n" ); document.write( "CANNOT BE OBTAINED FROM THE OTHER EQUATION BY BY ANY
\n" ); document.write( "SUITABLE AND PERMISSIBLE TRANSFORMATION .
\n" ); document.write( "or inconsistent.MEANS THERE ARE NO SET OF VALUES FOR X
\n" ); document.write( "AND Y WHICH SATISFY BOTH THE EQUATIONS.
\n" ); document.write( "3x-y=7.....I.......
\n" ); document.write( "6x-2Y=9..........II
\n" ); document.write( "what does these terms mean?NOW I THINK YOU KNOW WHAT
\n" ); document.write( "THE TERMS MEAN.THERE ARE TESTS FOR FINDING THESE
\n" ); document.write( "SITUATIONS.WE SHALL RESTRICT THE ANALYSIS TO YOUR
\n" ); document.write( "PROBLEM
\n" ); document.write( "WE FIND THAT ON L.H.S OF THE 2 EQNS.WE HAVE 3X-Y AND
\n" ); document.write( "6X-2Y WHICH ARE DIRECT MULTIPLES BY 2 .THAT IS WE GET
\n" ); document.write( "LHS OF EQN.2 BY MULTIPLYING THE EQN 1 WITH 2
\n" ); document.write( "WE GET EQN.I *2 ....6X-2Y=14
\n" ); document.write( "WHERE AS EQN.II SAYS 6X-2Y=9..SO IF WE TRY TO SATISFY
\n" ); document.write( "EQN.I ,EQN II WILL NOT BE SATISFIED AND IF WE TRY TO
\n" ); document.write( "SATISFY EQN II ,EQN.I WILL NOT BE SATISFIED.SO THERE
\n" ); document.write( "ARE NO VALUES OF X AND Y WHICH SATISFY BOTH
\n" ); document.write( "EQUATIONS.SO WE SAY THE GIVEN EQNS. ARE INCONSISTENT.
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\n" ); document.write( "Solve the following system by addition. If a unique
\n" ); document.write( "solution does not exist, state
\n" ); document.write( "whether the system is inconsistent or dependent.
\n" ); document.write( "x + 5y =
\n" ); document.write( "10...................................................I
\n" ); document.write( "-2x – 10y = -20.................................II
\n" ); document.write( "-2*EQN.I GIVES
\n" ); document.write( "-2X-10Y=-20....WHICH IS SAME AS EQN.II...
\n" ); document.write( "HENCE THEY ARE DEPENDENT EQUATIONS.
\n" ); document.write( "SO INEFFECT WE HAVE ONLY ONE EQN.TO SOLVE FOR 2
\n" ); document.write( "UNKOWNS.
\n" ); document.write( "HENCE WE SHALL HAVE INFINTE SOLUTIONS LIKE IN THIS
\n" ); document.write( "CASE
\n" ); document.write( "X=0....Y=2
\n" ); document.write( "X=10...Y=0...ETC..
\n" ); document.write( "IMPORTANT NOTE.
\n" ); document.write( "THEY HAVE INFINITE SOLUTIONS BUT NOT ANY AND EVERY
\n" ); document.write( "VALUE OF X AND Y.FOR EXAMPLE IF X=0 ,THEN Y HAS TO
\n" ); document.write( "EQUAL 2 ONLY NOT ANY OTHER VALUE.SO IT HAS INFINITE
\n" ); document.write( "SETS OF X AND Y PAIRS FOR ITS SOLUTION
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