document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=55978>Question 55978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have the equations<BR>\n" );
document.write( "3x+ y+2z=6<BR>\n" );
document.write( " x+ y+4z=3<BR>\n" );
document.write( "2x+3y+2z=2<BR>\n" );
document.write( "I'm supposed to solve using elimination. I've tried eliminating every variable but the answer is never right when i check it. Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37964 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=37964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve by elimination:<BR>\n" );
document.write( "E1) 3x+ y+2z=6<BR>\n" );
document.write( "E2)  x+ y+4z=3<BR>\n" );
document.write( "E3) 2x+3y+2z=2<BR>\n" );
document.write( "Eliminate the y in the E1) and E2), multiply E2) by -1 and add them together:<BR>\n" );
document.write( "-1(x+y+4z)=-1(3)<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "3x+y+2z=6<BR>\n" );
document.write( "-x-y-4z=-3<BR>\n" );
document.write( "__________<BR>\n" );
document.write( "2x+0y-2z=3<BR>\n" );
document.write( "E4) 2x-2z=3<BR>\n" );
document.write( "+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++<BR>\n" );
document.write( "Eliminate the y in E2) and E3), multiply E2 by -3 and add them together:<BR>\n" );
document.write( "-3(x+y+4z)=-3(3)<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "-3x-3y-12z=-9<BR>\n" );
document.write( "2x+3y+2z=2<BR>\n" );
document.write( "____________<BR>\n" );
document.write( "-x+0y-10z=-7<BR>\n" );
document.write( "E5) -x-10z=-7<BR>\n" );
document.write( "++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++<BR>\n" );
document.write( "Eliminate the x in E4) and E5), multiply  E5) by 2 and add them together:<BR>\n" );
document.write( "2(-x-10z)=2(-7)<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "2x-2z=3<BR>\n" );
document.write( "-2x-20z=-14<BR>\n" );
document.write( "_____________<BR>\n" );
document.write( "0x-22z=-11<BR>\n" );
document.write( "-22z=-11<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-22z%2F-22=-11%2F-22 ALIGN=MIDDLE  ALT=\"-22z%2F-22=-11%2F-22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "z=1/2<BR>\n" );
document.write( "+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++<BR>\n" );
document.write( "Sustitute z=1/2 into E5) and solve for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-10%281%2F2%29=-7 ALIGN=MIDDLE  ALT=\"-x-10%281%2F2%29=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-x-5=-7<BR>\n" );
document.write( "-x-5+5=-7+5<BR>\n" );
document.write( "-x=-2<BR>\n" );
document.write( "-(-x)=-(-2)<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++<BR>\n" );
document.write( "Substitute z=1/2 and x=2 into E1,E2, or E3 and solve for y.  I'm going with E2.<BR>\n" );
document.write( "(2)+y+4(1/2)=3<BR>\n" );
document.write( "2+y+2=3<BR>\n" );
document.write( "y+4=3<BR>\n" );
document.write( "y+4-4=3-4<BR>\n" );
document.write( "y=-1<BR>\n" );
document.write( "Therefore the solution is (x,y,z)=(2,-1,1/2)<BR>\n" );
document.write( "I'll leave it to you to check.  If you can't do that then let me know.  I checked it with a calculator.<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );