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You can put this solution on YOUR website!
I can't figure out how to solve this equation
\n" ); document.write( "6x-3y=1
\n" ); document.write( "-12x+6y=-2 I need to solve using a matrix but I can't figure out how to get the answer in the back of the book. It says the answer is (3y+1/6,y)
\n" ); document.write( "THESE ARE DEPENDENT EQNS..HENCE YOU MIGHT BE FACING THE DIFFICULTY
\n" ); document.write( "HOPE YOU KNOW THE METHOD
\n" ); document.write( "AUGMENTED MATRIX IS
\n" ); document.write( "....COEF.OF X.....COEF.OF Y.....CONSTANT......UNIT MATRIX
\n" ); document.write( "............6.......-3..............1...........1..............0
\n" ); document.write( "...........-12..... .6.............-2...........0..............1
\n" ); document.write( "
\n" ); document.write( "WE HAVE TO CONVERT IT NOW..
\n" ); document.write( "1.NEW R1=OLD R1/6
\n" ); document.write( "............1........-3/6...........1/6.........1/6.............0
\n" ); document.write( "............-12........6.............-2..........0..............1
\n" ); document.write( "2.NEW R2 =OLD R2+12*R1
\n" ); document.write( "............1.........-1/2...........1/6.........1/6.............0
\n" ); document.write( "............0..........0.............0............2..............1
\n" ); document.write( "NOW WE CANNOPT MAKE SECOND ROW ,SECOND COLUMN ELEMENT AS 1 ANY MORE AS IS NORMALLY DONE IN CONSISTENT AND INDEPENDENT EQN.
\n" ); document.write( "THE PRESENCE OF ZEROS IN ALL 3 COLUMNS IN SECOND ROW INDICATES THAT THE EQN.GIVEN ARE DEPENDENT .SO WE HAVE ONLY ONE INDEPENDENT EQN.IN 2 UNKNOWNS .HENCE WE SHALL NOT HAVE A UNIQUE SOLUTION.WE GET AN INFINITE SET OF ANSWERS .THEY ARE GIVEN BY FIRST ROW WHICH TELLS US THAT
\n" ); document.write( "1X-Y/2=1/6
\n" ); document.write( "SO TO GET ANY SET OF SOLUTION PUT X ANY VALUE AND FIND Y OR VICEVERSA.
\n" ); document.write( "SUPPOSE WE PUT X=0...THEN -Y/2=1/6...OR....Y=-2/6=-1/3...
\n" ); document.write( " SO SOLUTION SET IS (0,-1/3)
\n" ); document.write( "OR PUT X=1/6....THEN Y=0..
\n" ); document.write( "SO SOLUTION SET IS (*1/6,0)....ETC....
\n" ); document.write( "..SAME WAY WITH Y
\n" ); document.write( "PUT Y=0...THEN X=1/6....
\n" ); document.write( "SO SOLUTION SET IS (1/6,0)
\n" ); document.write( "IN GENERAL IF WE TAKE Y=Y..THEN 1X=Y/2+1/6 = (3Y+1)/6
\n" ); document.write( "SO THE SOLUTION SET IS
\n" ); document.write( "{(3Y+1)/6,Y}..THIS IS WHAT IS GIVEN IN YOUR BOOK.
\n" ); document.write( "IT MEANS PUT ANY VALUE FOR Y IN THIS SET AND THE RESULTANT NUMBERS WILL GIVE YOU A SOLUTION FOR THE GIVEN EQNS.
\n" ); document.write( "BUT YOU NEED NOT GIVE THIS ONLY AS AN ANSWER.FOR EX. YOU CAN PUT X=X AND THEN
\n" ); document.write( "X-Y/2=1/6...SO....Y/2=X-1/6....OR....Y=2X-1/3=(6X-1)/3...HENCE THE ANSWER COULD ALSO BE GIVEN AS {X,(6X-1)/3}...GOT IT?BUT YOU HAVE TO GIVE A GENERAL SOLUTION LIKE THIS AND NOT JUST 1 SET OF VALUES LIKE (0,-1/3) \n" ); document.write( "