document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250227>Question 250227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a 3-by-3 linear system, there should be a tripled pair for the system.\r<BR>\n" );
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document.write( "This system being:\r<BR>\n" );
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document.write( "3x+3y+6z=9<BR>\n" );
document.write( "2x+y+3z=7<BR>\n" );
document.write( "x+2y-z=-10\r<BR>\n" );
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document.write( "what would be the work in solving this? I figured out the tripled pair, but my work doesn't seem to match up exactly. Would you please help me with this problem? At least start me off, so I can finish it! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182158 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=182158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a 3-by-3 linear system, there should be a tripled pair for the system. <BR>\n" );
document.write( "This system being: <BR>\n" );
document.write( "3x+3y+6z=9<BR>\n" );
document.write( "2x+y+3z=7<BR>\n" );
document.write( "x+2y-z=-10 <BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Let the 3rd equation be 1st:<BR>\n" );
document.write( "x+2y-z=-10 <BR>\n" );
document.write( "3x+3y+6z=9<BR>\n" );
document.write( "2x+y+3z=7<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Multiply 1st by 3 and subtract from the 2nd:<BR>\n" );
document.write( "Multiply 1st be 2 and subtract from the 3rd:<BR>\n" );
document.write( "x+2y-z=-10 <BR>\n" );
document.write( "0-3y+9z=39<BR>\n" );
document.write( "0-3y+5z=27<BR>\n" );
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document.write( "Subtract the 2nd from the 3rd:<BR>\n" );
document.write( "x+2y-z=-10 <BR>\n" );
document.write( "0-3y+9z=39<BR>\n" );
document.write( "0-0y-4z=-12<BR>\n" );
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document.write( "Solve the 3rd equation for \"z\":<BR>\n" );
document.write( "z = 3<BR>\n" );
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document.write( "Substitute z=3 into the 2nd and solve for \"y\":<BR>\n" );
document.write( "-3y + 27 = 39<BR>\n" );
document.write( "-3y = 12<BR>\n" );
document.write( "y = -4<BR>\n" );
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document.write( "Substitute z=3 and y = -4 into the 1st and solve for \"x\":<BR>\n" );
document.write( "x + 2(-4)-(3) = -10<BR>\n" );
document.write( "x -8 - 3 = -10<BR>\n" );
document.write( "x -11 = -10<BR>\n" );
document.write( "x = 1<BR>\n" );
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document.write( "Final answer: x = 1 ; y = -4 ; z = 3<BR>\n" );
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document.write( "I checked this with a matrix method.<BR>\n" );
document.write( "It is correct.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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