document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249137>Question 249137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My son is having an impossible time with this question; we hope you can help.<BR>\n" );
document.write( "He has 3 line equations with 3 variables.<BR>\n" );
document.write( "5/x +3y + 62=1<BR>\n" );
document.write( "1/x +3(z-y)=9 1/5<BR>\n" );
document.write( "2/x +3/5z+y=-1\r<BR>\n" );
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document.write( "He has tried the Gaussian(sp) elimination method but cannot quite figure it out.<BR>\n" );
document.write( "Can you show him how to do this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181506 by </B><A HREF=/tutors/aboutme.mpl?userid=kensson><B>kensson(21)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kensson><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=kensson><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=181506\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can't use Gaussian elimination on a non-linear system. You have to do it with algebra.\r<BR>\n" );
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document.write( "(1) 5/x + 3y + 62 = 1<BR>\n" );
document.write( "(2) 1/x + 3(z-y) = 46/5<BR>\n" );
document.write( "(3) 2/x + 3z/5 + y = -1\r<BR>\n" );
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document.write( "Multiply it all through by 5x:\r<BR>\n" );
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document.write( "(1) 25 + 15xy = -305x<BR>\n" );
document.write( "(2) 5 + 15xz - 15xy = 46x<BR>\n" );
document.write( "(3) 10 + 3xz + 5xy = -5x<BR>\n" );
document.write( "3*(3) 30 + 9xz + 15xy = -15x\r<BR>\n" );
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document.write( "Add (1) and (2) -> (4)\r<BR>\n" );
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document.write( "(4) 30 + 15xz = -259x<BR>\n" );
document.write( "or:  x(15z + 259) = -30\r<BR>\n" );
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document.write( "Add (2) and 3*(3) -> (5)\r<BR>\n" );
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document.write( "(5) 35 + 24xz = 31x<BR>\n" );
document.write( "or: x(24z - 31) = -35\r<BR>\n" );
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document.write( "Isolate x and juggle to get:\r<BR>\n" );
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document.write( "-30(24z-31) = -35(15z + 259)\r<BR>\n" );
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document.write( "-720z + 930 = -525z - 9065\r<BR>\n" );
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document.write( "9995 = 195z\r<BR>\n" );
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document.write( "This gives z = 199/39*. You can sub that back into (4) or (5) to get x, and both into (1), (2) or (3) to get y.\r<BR>\n" );
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document.write( "* I don't believe this is the correct answer to the problem set, but the method is right.\r<BR>\n" );
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document.write( "===\r<BR>\n" );
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document.write( "EDIT\r<BR>\n" );
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document.write( "If the first line is 5/x +3y + 6z=1, it comes out more nicely.\r<BR>\n" );
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document.write( "5/x +3y + 6z=1<BR>\n" );
document.write( "1/x +3(z-y)=9 1/5<BR>\n" );
document.write( "2/x +3/5z+y=-1\r<BR>\n" );
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document.write( "Let w = 1/z\r<BR>\n" );
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document.write( "(1) 5w + 3y +   6z =  1<BR>\n" );
document.write( "(2)  w - 3y +   3z =  9.2<BR>\n" );
document.write( "(3) 2w +  y + 0.6z = -1\r<BR>\n" );
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document.write( "(1)          5w +  3y + 6z = 1<BR>\n" );
document.write( "(4) = 5*(2)  5w - 15y + 15z = 46<BR>\n" );
document.write( "(5) = 5*(3) 10w +  5y +  3z = -5\r<BR>\n" );
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document.write( "(6) = (1)-(4)    18y - 9z = -45<BR>\n" );
document.write( "(7) = 2*(1)-(5)    y + 9z =   7\r<BR>\n" );
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document.write( "(6)+(7) 19y = -38<BR>\n" );
document.write( "So y = -2<BR>\n" );
document.write( "From (7) -2 + 9z = 7 so z = 1<BR>\n" );
document.write( "From (2) w + 6 +3 = 9.2 so w = 0.2 and x = 5. </SPAN>\n" );
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