document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162861>Question 162861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by substitution or elimination:<BR>\n" );
document.write( "3x-4y+2z=-2<BR>\n" );
document.write( "5x-y+3z=1<BR>\n" );
document.write( "x+y-z=-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120066 by </B><A HREF=/tutors/aboutme.mpl?userid=elima><B>elima(1433)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=elima><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=120066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x-4y+2z=-2<BR>\n" );
document.write( "5x-y+3z=1<BR>\n" );
document.write( "x+y-z=-5<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "I'll go ahead and use elimination;<BR>\n" );
document.write( "Add 2 equations together to eliminate the y;<BR>\n" );
document.write( "5x-y+3z=1    <BR>\n" );
document.write( "x+y-z=-5<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "6x+2z=-4<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "now add together 2 other equations to eliminate the y;<BR>\n" );
document.write( "3x-4y+2z=-2<BR>\n" );
document.write( "x+y-z=-5 - multiply this equation by 4 so the y will eliminate;<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "4(x+y-z=-5)<BR>\n" );
document.write( "4x+4y-4z=-20<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "Now add the 2 equations;<BR>\n" );
document.write( "3x-4y+2z=-2<BR>\n" );
document.write( "4x+4y-4z=-20<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "7x-2z=-22<BR>\n" );
document.write( "================<BR>\n" );
document.write( "Now add the new equations together to eliminate a variable;<BR>\n" );
document.write( "6x+2z=-4<BR>\n" );
document.write( "7x-2z=-22<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "13x=-26<BR>\n" );
document.write( "x=-2<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Now we have what x equals, so we plug that into the equations then add them together to eliminate another variable;<BR>\n" );
document.write( "5x-y+3z=1<BR>\n" );
document.write( "x+y-z=-5<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "-10-y+3z=1<BR>\n" );
document.write( "-2+y-z=-5<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "-12+2z=-4<BR>\n" );
document.write( "2z=8<BR>\n" );
document.write( "z=4<BR>\n" );
document.write( "===========<BR>\n" );
document.write( "Now that we have both x and z we can plug those into any equation and find y;<BR>\n" );
document.write( "x+y-z=-5<BR>\n" );
document.write( "-2+y-4=-5<BR>\n" );
document.write( "-6+y=-5<BR>\n" );
document.write( "y=1<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "Check;<BR>\n" );
document.write( "-2+1-4=-5<BR>\n" );
document.write( "-1-4=-5<BR>\n" );
document.write( "-5=-5<BR>\n" );
document.write( "check;<BR>\n" );
document.write( "5x-y+3z=1<BR>\n" );
document.write( "-10-1+12=1<BR>\n" );
document.write( "-11+12=1<BR>\n" );
document.write( "1=1<BR>\n" );
document.write( ":)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );