document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014596>Question 1014596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve:<BR>\n" );
document.write( " x-6y-2z=-8<BR>\n" );
document.write( "-x+5y+3z=2<BR>\n" );
document.write( "3x-2y-4z=18<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630920 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=630920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x-6y-2z=-8<BR>\n" );
document.write( "-x+5y+3z=2<BR>\n" );
document.write( "3x-2y-4z=18<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "x-6y-2z=-8<BR>\n" );
document.write( "-x+5y+3z=2<BR>\n" );
document.write( "----------<BR>\n" );
document.write( " -y+z= -6<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "x-6y-2z=-8<BR>\n" );
document.write( "3x-2y-4z=18<BR>\n" );
document.write( "On the first equation multiply all terms by -3:<BR>\n" );
document.write( "-3x+18y+6z= 24 <BR>\n" );
document.write( "Add the equations:<BR>\n" );
document.write( "-3x+18y+6z= 24<BR>\n" );
document.write( "3x-2y-4z= 18<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "16y+2z= 42<BR>\n" );
document.write( "Now we have two new equations:<BR>\n" );
document.write( "-y+z= -6<BR>\n" );
document.write( "16y+2z= 42<BR>\n" );
document.write( "Multiply the 1st equation times -2<BR>\n" );
document.write( "2y-2z= 12<BR>\n" );
document.write( "Add equations<BR>\n" );
document.write( "16y+2z= 42<BR>\n" );
document.write( "2y-2z= 12<BR>\n" );
document.write( "18y= 54 Divide both sides by 18<BR>\n" );
document.write( "y= 3 Now we know the value of y.<BR>\n" );
document.write( "Take one of the last two equations and find z:<BR>\n" );
document.write( "16y+2z= 42<BR>\n" );
document.write( "16(3)+2z= 42<BR>\n" );
document.write( "48+2z= 42<BR>\n" );
document.write( "2z= -6<BR>\n" );
document.write( "z= -3<BR>\n" );
document.write( "You say, what if I chose the other equation to find z? Well:<BR>\n" );
document.write( "2y-2z= 12<BR>\n" );
document.write( "2(3)-2z= 12<BR>\n" );
document.write( "6-2z= 12<BR>\n" );
document.write( "-2z= 6<BR>\n" );
document.write( "z= -3 Same answer. Cool, no?<BR>\n" );
document.write( "Now we know y and z, let's go back to one of the original equations to find x:<BR>\n" );
document.write( "x-6y-2z=-8<BR>\n" );
document.write( "x-6(3)-2(-3)= -8<BR>\n" );
document.write( "x-18+6= -8<BR>\n" );
document.write( "x-12= -8<BR>\n" );
document.write( "x= 4<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "Am I right? Let's check:<BR>\n" );
document.write( "x-6y-2z=-8; 4-6(3)-2(-3)= -8; 4-18+6= 8; -18+10= -8 Correct<BR>\n" );
document.write( "-x+5y+3z=2; -4+5(3)+3(-3)= 2; -4+15-9= 2; 11-9= 2 correct<BR>\n" );
document.write( "3x-2y-4z=18; 3(4)-2(3)-4(-3)= 18; 12-6+12= 18; 6+12= 18 Correct<BR>\n" );
document.write( "We have the correct answers.<BR>\n" );
document.write( "J\r<BR>\n" );
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