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Question 44737This question is from textbook College Algebra
: Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent.
2y = 1 - 4x
2x + y = 0
This question is from textbook College Algebra
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE THE FOLLOWING AND TRY
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SEE
\solve each of the follwing systems by substitution.
5x-2y=-5............I
y-5x=3......................II...Y=3+5X..........PUT IN EQN.I
5X-2(3+5X)=-5
5X-6-10X=-5
-5X=6-5=1
X=-1/5
Y=3+5X=3+5*(-1/5)=3-1=2
THESE ARE CONSISTENT INDEPENDENT EQNS.AND HENCE HAVE A UNIQUE SOLUTUIN NAMELY...
=-1/5 AND Y=2THE FOLLOWING AND TRY
Equations/44050: solve each of the following systems by graphing
3x-6y=9
x-2y=3
1 solutions
Answer 28988 by venugopalramana(2194) About Me on 2006-06-28 00:45:24 (Show Source):
You can put this solution on YOUR website!
SEE THE FOLLOWING AND TRY
solve each of the following systems by sustitution.
8x-4y=16....................I
y=2x-4....................II....PUT THIS IN EQN.I
8X-4(2X-4)=16
8X-8X+16=16
16=16.....OK...
HENCE THE EQNS.ARE DEPENDENT ANE THERE ARE INFINITE SETS OF SOLUTIONS..ANY SET WITH
X=ANY VALUE......SAY'0'
AND Y=2X-4=2*0-4=-4 IS A SOLUTION SET.
YOU CAN GIVE ANY VALUE TO X,FIND CORRESPONDING Y AND THAT IS THE SOLUTION SET.
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.
2x+3y=1
5x+3y=16
1 solutions
Answer 28987 by venugopalramana(2194) About Me on 2006-06-28 00:44:02 (Show Source):
You can put this solution on YOUR website!
SEE THE FOLLOWING AND TRY
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solve each of the follwing systems by substitution.
5x-2y=-5............I
y-5x=3......................II...Y=3+5X..........PUT IN EQN.I
5X-2(3+5X)=-5
5X-6-10X=-5
-5X=6-5=1
X=-1/5
Y=3+5X=3+5*(-1/5)=3-1=2
THESE ARE CONSISTENT INDEPENDENT EQNS.AND HENCE HAVE A UNIQUE SOLUTUIN NAMELY...
=-1/5 AND Y=2
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.
x+5y=10
-2x-10y=-20
1 solutions
Answer 28986 by venugopalramana(2194) About Me on 2006-06-28 00:42:35 (Show Source):
You can put this solution on YOUR website!
SEE THE FOLLOWING AND TRY
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solve each of the following systems by sustitution.
8x-4y=16....................I
y=2x-4....................II....PUT THIS IN EQN.I
8X-4(2X-4)=16
8X-8X+16=16
16=16.....OK...
HENCE THE EQNS.ARE DEPENDENT ANE THERE ARE INFINITE SETS OF SOLUTIONS..ANY SET WITH
X=ANY VALUE......SAY'0'
AND Y=2X-4=2*0-4=-4 IS A SOLUTION SET.
YOU CAN GIVE ANY VALUE TO X,FIND CORRESPONDING Y AND THAT IS THE SOLUTION SET.
Equations/44055: solve each of the follwing systems by substitution.
5x-2y=-5
y-5x=3
1 solutions
Answer 28985 by venugopalramana(2194) About Me on 2006-06-28 00:39:28 (Show Source):
You can put this solution on YOUR website!
solve each of the follwing systems by substitution.
5x-2y=-5............I
y-5x=3......................II...Y=3+5X..........PUT IN EQN.I
5X-2(3+5X)=-5
5X-6-10X=-5
-5X=6-5=1
X=-1/5
Y=3+5X=3+5*(-1/5)=3-1=2
THESE ARE CONSISTENT INDEPENDENT EQNS.AND HENCE HAVE A UNIQUE SOLUTUIN NAMELY...
=-1/5 AND Y=2
Equations/44056: solve each of the following systems by sustitution.
8x-4y=16
y=2x-4
1 solutions
Answer 28984 by venugopalramana(2194) About Me on 2006-06-28 00:35:11 (Show Source):
You can put this solution on YOUR website!
solve each of the following systems by sustitution.
8x-4y=16....................I
y=2x-4....................II....PUT THIS IN EQN.I
8X-4(2X-4)=16
8X-8X+16=16
16=16.....OK...
HENCE THE EQNS.ARE DEPENDENT ANE THERE ARE INFINITE SETS OF SOLUTIONS..ANY SET WITH
X=ANY VALUE......SAY'0'
AND Y=2X-4=2*0-4=-4 IS A SOLUTION SET.
YOU CAN GIVE ANY VALUE TO X,FIND CORRESPONDING Y AND THAT IS THE SOLUTION SET.
Equations/44057: solve each of the following systmes by substitution.
4x-12y=5
-x+3y=-1
1 solutions
Answer 28983 by venugopalramana(2194) About Me on 2006-06-28 00:31:42 (Show Source):
You can put this solution on YOUR website!
solve each of the following systmes by substitution.
4x-12y=5................I
-x+3y=-1...............II.....X=3Y+1..PUT THIS IN EQN.I
4(3Y+1)-12Y=5
12Y+4-12Y=5
4=5...NOT POSSIBLE
HENCE EQNS. ARE INCONSISTENT AND THERE IS NO SOLUTION
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.
10x+2y=7
y=-5x+3
1 solutions
Answer 28982 by venugopalramana(2194) About Me on 2006-06-28 00:22:33 (Show Source):
You can put this solution on YOUR website!
SEE THE FOLLOWING AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK
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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-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
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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Solve the following system by addition. If a unique
solution does not exist, state
whether the system is inconsistent or dependent.
x + 5y =
10...................................................I
-2x – 10y = -20.................................II
-2*EQN.I GIVES
-2X-10Y=-20....WHICH IS SAME AS EQN.II...
HENCE THEY ARE DEPENDENT EQUATIONS.
SO INEFFECT WE HAVE ONLY ONE EQN.TO SOLVE FOR 2
UNKOWNS.
HENCE WE SHALL HAVE INFINTE SOLUTIONS LIKE IN THIS
CASE
X=0....Y=2
X=10...Y=0...ETC..
IMPORTANT NOTE.
THEY HAVE INFINITE SOLUTIONS BUT NOT ANY AND EVERY
VALUE OF X AND Y.FOR EXAMPLE IF X=0 ,THEN Y HAS TO
EQUAL 2 ONLY NOT ANY OTHER VALUE.SO IT HAS INFINITE
SETS OF X AND Y PAIRS FOR ITS SOLUTION
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