document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142658>Question 1142658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My book says this is for systems of equations in three variables, the elimination method. Question: How do I solve 2r+3s+12t=4,4r-6s+6t=1,r+s+t=1?  I have tried to combine the first 2 formulas, eliminating opposites and collecting like terms and then using that answer to add to the third formula(r,s,t=1) but there are no opposites. I'm stumped. Please and thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763362 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) 2r +3s +12t = 4<BR>\n" );
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document.write( "2) 4r -6s +6t = 1<BR>\n" );
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document.write( "3) r +s +t = 1<BR>\n" );
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document.write( "multiply equation 3 by 6 and add to equation 2 to eliminate variable s<BR>\n" );
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document.write( "4) 10r +12t = 7<BR>\n" );
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document.write( "multiply equation 1 by 2 and add to equation 2 to sliminate variable s<BR>\n" );
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document.write( "5) 8r +30t = 9<BR>\n" );
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document.write( "solve equations 4 and 5 for r and t<BR>\n" );
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document.write( "solve equation 5 for r and substitute in equation 4<BR>\n" );
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document.write( "r = (9 -30t)/8<BR>\n" );
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document.write( "10(9 -30t)/8 +12t = 7<BR>\n" );
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document.write( "90 -300t +96t = 56<BR>\n" );
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document.write( "-204t = -34<BR>\n" );
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document.write( "t = 34/204 = 17/102<BR>\n" );
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document.write( "r = (9 -30(17/102))/8 = 1/2<BR>\n" );
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document.write( "use equation 3 to solve for s<BR>\n" );
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document.write( "1/2 +s +17/102 = 1<BR>\n" );
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document.write( "s = 34/102 = 1/3<BR>\n" );
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document.write( "r = 1/2, s = 1/3, t = 17/102<BR>\n" );
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document.write( "check the answers<BR>\n" );
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document.write( "equation 1<BR>\n" );
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document.write( "2(1/2) +3(1/3) +12(17/102) = 4<BR>\n" );
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document.write( "1 +1 +2 = 4<BR>\n" );
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document.write( "4 = 4<BR>\n" );
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document.write( "equation 2<BR>\n" );
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document.write( "4(1/2) -6(1/3) +6(17/102) = 1<BR>\n" );
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document.write( "2 -2 +1 = 1<BR>\n" );
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document.write( "1 = 1<BR>\n" );
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document.write( "equation 3<BR>\n" );
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document.write( "1/2 +1/3 +17/102 = 1<BR>\n" );
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document.write( "51/102 + 34/102 +17/102 = 1<BR>\n" );
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document.write( "102/102 = 1<BR>\n" );
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document.write( "1 = 1<BR>\n" );
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document.write( "answers check<BR>\n" );
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