document.write( "Question 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( "
Algebra.Com's Answer #28982 by venugopalramana(3286)\"\" \"About 
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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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\n" ); document.write( "2x+y=4
\n" ); document.write( "3x-y=6
\n" ); document.write( "make a deteminant with coefficients of x (2,3)and
\n" ); document.write( "y(1,-1) in the 2 eqns.call it C.(Actually for a
\n" ); document.write( "determinant as you know ,the numbers are contained in
\n" ); document.write( "vertical bars at either end like |xx|,but in the
\n" ); document.write( "following the bars are omitted due to difficulty in
\n" ); document.write( "depiction.you may assume the bars are present)
\n" ); document.write( "C=matrix(2,2,2,1,3,-1)=2*(-1)-(1*3)=-5
\n" ); document.write( "..now use the constants (4,6)to replace coefficients
\n" ); document.write( "of x(2,3) in the above determinant C...call it CX..
\n" ); document.write( "CX=matrix(2,2,4,1,6,-1)=4*(-1)-1*6=-4-6=-10
\n" ); document.write( "..now use the constants (4,6)to replace coefficients
\n" ); document.write( "of y(1,-1) in the above determinant C...call it CY..
\n" ); document.write( "CY=matrix(2,2,2,4,3,6)=2*6-3*4=12=12=0
\n" ); document.write( "..now cramers rule says that
\n" ); document.write( "(x/CX)=(y/CY)=(1/C)..so we get
\n" ); document.write( "x/(-10)=y/0=1/-5
\n" ); document.write( "x=-10/-5=10/5=2
\n" ); document.write( "y=0/-5=0
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\n" ); document.write( "............... 3x+5y=17
\n" ); document.write( "................. x+3y=15
\n" ); document.write( "D=DETERMINANT OF COEFFICIENT
\n" ); document.write( "D =DET|3,5|
\n" ); document.write( "............|1,3|=3*3-1*5=9-5=4
\n" ); document.write( "DX=DET|17,5|
\n" ); document.write( "............|15,3|=17*3-5*15=51-75=-24
\n" ); document.write( "DY=DET|3,17|
\n" ); document.write( ".............|1,15|=3*15-17*1=45-17=28
\n" ); document.write( "X/DX=Y/DY=1/D
\n" ); document.write( "X=DX/D=-24/4=-6
\n" ); document.write( "Y=DY/D=28/4=7 \n" ); document.write( "
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