document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1053040>Question 1053040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three numbers such that: their sum is 12;the sum of the first, twice the second, and three times the third is 31;the sum of the third and nine times the second is 1.<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 #807714 by </B><A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><B>CubeyThePenguin(3113)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><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=CubeyThePenguin><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807714\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + y + z = 12<BR>\n" );
document.write( "x + 2y + 3z = 31<BR>\n" );
document.write( "9y + z = 1 ----> z = 1 - 9y\r<BR>\n" );
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document.write( "Substitute the expression for z into the first two equations.\r<BR>\n" );
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document.write( "x + y + (1 - 9y) = 12 ---> x - 8y = 11<BR>\n" );
document.write( "x + 2y + 3(1 - 9y) = 31 ---> x - 25y = 28\r<BR>\n" );
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document.write( "Subtract the equations to get\r<BR>\n" );
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document.write( "x - 8y = 11<BR>\n" );
document.write( "-x + 25y = -28<BR>\n" );
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document.write( "17y = -17<BR>\n" );
document.write( "y = -1\r<BR>\n" );
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document.write( "9y + z = 1<BR>\n" );
document.write( "9(-1) + z = 1 ---> z = 10\r<BR>\n" );
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document.write( "x + (-1) + 10 = 12<BR>\n" );
document.write( "x = 3\r<BR>\n" );
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document.write( "solution: (x, y, z) = (3, -1, 10) </SPAN>\n" );
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