document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389508>Question 389508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve for a system of three variables, and this is the first time I've ever came across this so I don't really know if I'm doing this right...\r<BR>\n" );
document.write( "\n" );
document.write( "So here is the system:<BR>\n" );
document.write( "2x - y + 3z = 8<BR>\n" );
document.write( "x - 6y - z = 0<BR>\n" );
document.write( "-6x + 3y - 9z = 24 \r<BR>\n" );
document.write( "\n" );
document.write( "I decided to get x taken care of first so I took the middle equation and it made x = 6y + z<BR>\n" );
document.write( "And then I took x and plugged it in to the top equation so it would be 2(6y+z) - y + 3z = 8 and then it went to 12y + 2z - y + 3z = 8 and then 11y + 5z = 8 and then I got y = 5/11z +8/11 <BR>\n" );
document.write( "Then to get z I went ahead and plugged in x and y into the third equation, (which is where I think I made the wrong move...) then I got -36y - 6z + 15/11z + 24/11 - 9z = 24<BR>\n" );
document.write( "Added like terms, and then that's where I got stumped. -6z + 15/11z is 9/11z, and then when you add the -9z it makes 0/11z? and if I actually did solve for z I really wouldn't get the first solution... <BR>\n" );
document.write( "Can someone please help me point out where I went wrong and help me through this problem??? Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276013 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=276013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x - y + 3z = 8......................1<BR>\n" );
document.write( "x - 6y - z = 0.......................2<BR>\n" );
document.write( "-6x + 3y - 9z = 24 ..................3\r<BR>\n" );
document.write( "\n" );
document.write( "..<BR>\n" );
document.write( "select (1) &(2) eliminate x<BR>\n" );
document.write( "select (2)&(3) eliminate x<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Then solve for y & z<BR>\n" );
document.write( "multiply (2) by -2 and add to (1)\r<BR>\n" );
document.write( "\n" );
document.write( "-2x+12y+2z=0<BR>\n" );
document.write( "Add<BR>\n" );
document.write( "+11y+5z=8......................(3)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "consider (2)&(3) eliminate x<BR>\n" );
document.write( "multiply (2)by 6 and add to (3)<BR>\n" );
document.write( "6x-36y-6z=0<BR>\n" );
document.write( "add<BR>\n" );
document.write( "-33y-7z=24.....................(4)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "multiply (3) by 3 & add to 4<BR>\n" );
document.write( "33y+15z=24<BR>\n" );
document.write( "add<BR>\n" );
document.write( "+8z=48<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28z=6%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28z=6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "plug z= 6 in (3)<BR>\n" );
document.write( "11y+5*6=8<BR>\n" );
document.write( "11y+30=8<BR>\n" );
document.write( "11y=-22<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28y=-2%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28y=-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "plug y & z to get x<BR>\n" );
document.write( "2x - y + 3z = 8......................1<BR>\n" );
document.write( "2x+2+18=8<BR>\n" );
document.write( "2x+20=8<BR>\n" );
document.write( "2x=-12<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28x=-6%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28x=-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m.ananth@hotmail.ca </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );