document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54436>Question 54436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help.  Solve the following system by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent.<BR>\n" );
document.write( "10x + 2y = 7   and   y = -5x + 3<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #36700 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=36700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE THE FOLLOWING EXAMPLES AND TRY IF STILL IN DIFFICULTY PLEASE COME BACK<BR>\n" );
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document.write( "Solve the following system by addition. If a unique<BR>\n" );
document.write( "solution does not exist, state<BR>\n" );
document.write( "whether the system is inconsistent or dependent.<BR>\n" );
document.write( "x + 5y =10...........................................I<BR>\n" );
document.write( "-2x - 10y = -20.................................II<BR>\n" );
document.write( "-2*EQN.I GIVES<BR>\n" );
document.write( "-2X-10Y=-20....WHICH IS SAME AS EQN.II...<BR>\n" );
document.write( "HENCE THEY ARE DEPENDENT EQUATIONS.<BR>\n" );
document.write( "SO INEFFECT WE HAVE ONLY ONE EQN.TO SOLVE FOR 2<BR>\n" );
document.write( "UNKOWNS.<BR>\n" );
document.write( "HENCE WE SHALL HAVE INFINTE SOLUTIONS LIKE IN THIS<BR>\n" );
document.write( "CASE<BR>\n" );
document.write( "X=0....Y=2<BR>\n" );
document.write( "X=10...Y=0...ETC..<BR>\n" );
document.write( "IMPORTANT NOTE.<BR>\n" );
document.write( "THEY HAVE INFINITE SOLUTIONS BUT NOT ANY AND EVERY<BR>\n" );
document.write( "VALUE OF X AND Y.FOR EXAMPLE IF X=0 ,THEN Y HAS TO<BR>\n" );
document.write( "EQUAL 2 ONLY NOT ANY OTHER VALUE.SO IT HAS INFINITE<BR>\n" );
document.write( "SETS OF X AND Y PAIRS FOR ITS SOLUTION<BR>\n" );
document.write( "ANOTHER EXAMPLE IS<BR>\n" );
document.write( "X+Y=1........................1<BR>\n" );
document.write( "2X+2Y=2..............................2<BR>\n" );
document.write( "HERE AGIN EQN.2IS JUST A MULTIPLICATION OF EQN.1 WITH 2 ON BOTH LHS AND RHS<BR>\n" );
document.write( "THE GERAL SOLUTION FORMULA IS Y=1-X...OR (X,1-X)IS A<BR>\n" );
document.write( "SOLUTION SET..LIKE (1,0),(2,-1) ETC....<BR>\n" );
document.write( "THUS DEPENDENT EQNS.HAVE LHS AND RHS IN THE SAME PRPORTION OR COMBINATION IN DIFFERENT EQNS.  <BR>\n" );
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document.write( "AS THE NAME IMPLIES AN INCONSISTENT SET OF EQUATIONS<BR>\n" );
document.write( "HAS NO SOLUTION AS THEY ARE INCONSISTENT.FOR EXAMPLE<BR>\n" );
document.write( "X+Y=2.....................1<BR>\n" );
document.write( "2X+2Y=3.....................2<BR>\n" );
document.write( "IF WE TRY TO SATISFY EQN.1,WE CANT SATISFY EQN.2 AND VICEVERSA...AS THE LHS OF BOTH EQNS.ARE INPROPORTION OF 1:2,WHERE AS RHS IS IN THE RATIO OF 2:3<BR>\n" );
document.write( "HENCE THERE IS NO QUESTION OF GETTING A<BR>\n" );
document.write( "GENERAL SOLUTION FOR THAT BY ANY METHOD .<BR>\n" );
document.write( "SO INCONSISTENT EQNS HAVE LHS AS MULTIPLES OR COMBINATIONS IN ONE PROPORTION WHILE RHS IS IN DIFFERENT PROPORTION IN DIFFERENT EQNS.<BR>\n" );
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document.write( "FINALLY CONSISTENT AND INDEPENDENT EQNS.HAVE UNIQUE<BR>\n" );
document.write( "SOLUTION..FOR EXAMPLE<BR>\n" );
document.write( "X+Y=2...................1<BR>\n" );
document.write( "X-Y=0..........................2<BR>\n" );
document.write( "EQN.1 +EQN.2 GIVES <BR>\n" );
document.write( "2X=2...OR...X=1<BR>\n" );
document.write( "SUBSTITUTING IN EQN.1 ,WE GET Y=1.THUS THEY <BR>\n" );
document.write( "HAVE ONE UNIQUE SOLUTION X=1 AND Y=1<BR>\n" );
document.write( "HERE LHS OF DIFFERENT EQNS.IS NOT A DIRECT MULTIPLE OR COMBINATIONS OF OTHER EQNS.<BR>\n" );
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