document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358078>Question 358078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello, we are working with linear equations. i am trying to solve 3 equations with 3 variables each x,y, and z but the substitution method is not working for me. here are equations:<BR>\n" );
document.write( "x - y + 3z = 8<BR>\n" );
document.write( "3x + y - 2z = -2<BR>\n" );
document.write( "2x + 4y + z = 0<BR>\n" );
document.write( "I don't really want answers i need to see how. thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255609 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=255609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There's more than one way.  I'll use elimination.<BR>\n" );
document.write( "Look for coefficients that make it easiest to eliminate one of the 3 variables.<BR>\n" );
document.write( "x - y + 3z = 8<BR>\n" );
document.write( "3x + y - 2z = -2<BR>\n" );
document.write( "2x + 4y + z = 0<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "1*y is in the 1st and 2nd, so eliminate it first<BR>\n" );
document.write( "x - y + 3z = 8<BR>\n" );
document.write( "3x + y - 2z = -2<BR>\n" );
document.write( "------------------ Add<BR>\n" );
document.write( "4x + z = 6 <BR>\n" );
document.write( "Multiply eqn 1 by 4<BR>\n" );
document.write( "4x - 4y +12z = 32<BR>\n" );
document.write( "2x + 4y + z = 0<BR>\n" );
document.write( "----------------- Add<BR>\n" );
document.write( "6x + 13z = 32<BR>\n" );
document.write( "Now the x's can be eliminated<BR>\n" );
document.write( "Multiply 4x + z = 6 by 3 and the other by 2<BR>\n" );
document.write( "12x + 3z = 18<BR>\n" );
document.write( "12x +26z = 64<BR>\n" );
document.write( "-------------- Subtract<BR>\n" );
document.write( "-23z = -46<BR>\n" );
document.write( "z = 2<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Sub for z in 4x + z = 6<BR>\n" );
document.write( "--> x = 1<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Sub for x and z in one of the original eqns to find y.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );