document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162864>Question 162864</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by substitution or elimination:<BR>\n" );
document.write( "2x-3y+z=14<BR>\n" );
document.write( "4x+2y-5z=-3<BR>\n" );
document.write( "x+y+2z=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120071 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=120071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll use elimination to solve;<BR>\n" );
document.write( "2x-3y+z=14<BR>\n" );
document.write( "4x+2y-5z=-3<BR>\n" );
document.write( "x+y+2z=1<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "First add two equations together to eliminate a variable;<BR>\n" );
document.write( "4x+2y-5z=-3 - multiply equation by 2 so you can eliminate the z;<BR>\n" );
document.write( "x+y+2z=1  - multiply equation by 5 so you can eliminate the z;<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "2(4x+2y-5s=-3)<BR>\n" );
document.write( "8x+4y-10z=-6<BR>\n" );
document.write( "5(x+y+2z=1)<BR>\n" );
document.write( "5x+5y+10z=5<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "8x+4y-10z=-6<BR>\n" );
document.write( "5x+5y+10z=5<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "13x+9y=-1<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Now choose two others to eliminate the z;<BR>\n" );
document.write( "2x-3y+z=14 - multiply by -2<BR>\n" );
document.write( "x+y+2z=1<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "-2(2x-3y+z=14)<BR>\n" );
document.write( "-4x+6y-2z=-28<BR>\n" );
document.write( "x+y+2z=1<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "-3x+7y=-27<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Now add the two new equations together to eliminate another variable;<BR>\n" );
document.write( "13x+9y=-1 - multiply by -7<BR>\n" );
document.write( "-3x+y=-27 - multiply by 9<BR>\n" );
document.write( "============================<BR>\n" );
document.write( "-7(13x+9y=-1)<BR>\n" );
document.write( "-91x-63y=-14<BR>\n" );
document.write( "9(-3x+7y=-27)<BR>\n" );
document.write( "-21x+63y=-243<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "-91x-63y=7<BR>\n" );
document.write( "-27x+63y=-243<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "-118x=-236<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Now that we have the x, let's plug it into one of the new equations and solve for y;<BR>\n" );
document.write( "13(2)+9y=-1<BR>\n" );
document.write( "26+9y=-1<BR>\n" );
document.write( "9y=-27<BR>\n" );
document.write( "y=-3<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "We have our x and y, let's plug them in and get the z;<BR>\n" );
document.write( "x+y+2z=1<BR>\n" );
document.write( "2+-3+2z=1<BR>\n" );
document.write( "-1+2z=1<BR>\n" );
document.write( "2z=2<BR>\n" );
document.write( "z=1<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "check;<BR>\n" );
document.write( "2x-3y+z=14<BR>\n" );
document.write( "2(2)-3(-3)+1=14<BR>\n" );
document.write( "4+9+1=14<BR>\n" );
document.write( "14=14<BR>\n" );
document.write( "check;<BR>\n" );
document.write( "4x+2y-5z=-3<BR>\n" );
document.write( "4(2)+2(-3)-5(1)=-3<BR>\n" );
document.write( "8-6-5=-3<BR>\n" );
document.write( "-3=-3<BR>\n" );
document.write( ":)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );