document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=766025>Question 766025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello can you help me with this problem? It says you have to use the subsitution method to solve a system of equations that has three variables.\r<BR>\n" );
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document.write( "6x-4y+5z=31<BR>\n" );
document.write( "5x+2y+2z=13<BR>\n" );
document.write( "x+y+z=2\r<BR>\n" );
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document.write( "x=?<BR>\n" );
document.write( "y=?<BR>\n" );
document.write( "z=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466639 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=466639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6x-4y+5z=31<BR>\n" );
document.write( "5x+2y+2z=13<BR>\n" );
document.write( "x+y+z=2 <BR>\n" );
document.write( "========================================================================<BR>\n" );
document.write( "x+y+z=2<BR>\n" );
document.write( "solve for z<BR>\n" );
document.write( "z=2-x-y<BR>\n" );
document.write( "==================================================================<BR>\n" );
document.write( "substitute for z in second equation<BR>\n" );
document.write( "5x+2y+2*(2-x-y)=13<BR>\n" );
document.write( "5x+2y+4-2x-2y=13<BR>\n" );
document.write( "3x=9<BR>\n" );
document.write( "x=3<BR>\n" );
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document.write( "substitute for z and x in equation 1<BR>\n" );
document.write( "6*3 -4y +5*(2-3-y)=31<BR>\n" );
document.write( "18 -4y +10 -15 -5y = 31<BR>\n" );
document.write( "-9y +13 = 31<BR>\n" );
document.write( "-9y = 18<BR>\n" );
document.write( "y = -2<BR>\n" );
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document.write( "substitute x=3 and y=-2 into third equation<BR>\n" );
document.write( "3-2+z=2<BR>\n" );
document.write( "1+z=2<BR>\n" );
document.write( "z=1<BR>\n" );
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document.write( "check values in first, second and third equations<BR>\n" );
document.write( "6*3 -4*(-2) +5*1 = 31<BR>\n" );
document.write( "18 +8 +5 = 31<BR>\n" );
document.write( "31 = 31     equation 1 checks<BR>\n" );
document.write( "++++++++++++++++++++++++++++++++++++++++<BR>\n" );
document.write( "5*3 +2*(-2) + 2*1 = 13<BR>\n" );
document.write( "15 -4 +2 = 13<BR>\n" );
document.write( "13 = 13     equation 2 checks<BR>\n" );
document.write( "+++++++++++++++++++++++++++++++++++++++++<BR>\n" );
document.write( "3 -2 + 1 = 2<BR>\n" );
document.write( "2 = 2       equation 3 checks<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "x=3, y=-2, z=1\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );