document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159233>Question 159233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,-<BR>\n" );
document.write( "I have a problem with substitution that does not allow the use of matrices:\r<BR>\n" );
document.write( "\n" );
document.write( "2x + y = -2<BR>\n" );
document.write( "-x + 3y - 4z = -26<BR>\n" );
document.write( "5x - 6y + z = 17\r<BR>\n" );
document.write( "\n" );
document.write( "I started by solving for y in the first equation: y = -2 - 2x<BR>\n" );
document.write( "I then solved for x in the second equation: 3y -4z +26 = x<BR>\n" );
document.write( "I plugged the x and y values into the third equation<BR>\n" );
document.write( "                  5(3(-2-2x) - 6(-2 - 2x) + z = 17<BR>\n" );
document.write( "                  5(-6 -6x) + 12 + 12x + z = 17<BR>\n" );
document.write( "                  -30 + 30x + 12 + 12x + z = 17<BR>\n" );
document.write( "                  42 x + z -18 = 17<BR>\n" );
document.write( "                  42x + z = 35<BR>\n" );
document.write( "                  z = 35 - 42x<BR>\n" );
document.write( "Now I'm stuck.\r<BR>\n" );
document.write( "\n" );
document.write( "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 #117370 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=117370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, I have a problem with substitution that does not allow the use of matrices: <BR>\n" );
document.write( "2x + y = -2<BR>\n" );
document.write( "-x + 3y - 4z = -26<BR>\n" );
document.write( "5x - 6y + z = 17 <BR>\n" );
document.write( "I started by solving for y in the first equation: y = -2 - 2x<BR>\n" );
document.write( "I then solved for x in the second equation: 3y -4z +26 = x<BR>\n" );
document.write( "I plugged the x and y values into the third equation<BR>\n" );
document.write( "5(3(-2-2x) - 6(-2 - 2x) + z = 17<BR>\n" );
document.write( "5(-6 -6x) + 12 + 12x + z = 17<BR>\n" );
document.write( "-30 + 30x + 12 + 12x + z = 17   (should be -30x)<BR>\n" );
document.write( "42 x + z -18 = 17<BR>\n" );
document.write( "-18x + z = 35<BR>\n" );
document.write( "z = 35 + 18x <BR>\n" );
document.write( "Now I'm stuck. <BR>\n" );
document.write( "Thank you.<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Since there's no z term in the 1st eqn, sub for y in eqns 2 & 3.  Then you'll have 2 eqns in 2 unknowns.<BR>\n" );
document.write( "I started by solving for y in the first equation: y = -2 - 2x<BR>\n" );
document.write( "-x + 3y - 4z = -26<BR>\n" );
document.write( "5x - 6y + z = 17 <BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "-x + 3(-2-2x) -4z = -26<BR>\n" );
document.write( "5x -6(-2-2x) +z = 17<BR>\n" );
document.write( "collect terms<BR>\n" );
document.write( "-x -6-6x -4z = -26<BR>\n" );
document.write( "5x +12 +12x +z = 17<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "-7x -4z = -20<BR>\n" );
document.write( "17x + z = 5<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Take the easy one, z = 5-17x<BR>\n" );
document.write( "Sub into -7x -4z = -20<BR>\n" );
document.write( "-7x -4(5-17x) = -20<BR>\n" );
document.write( "-7x -20 + 68x = -20<BR>\n" );
document.write( "61x = 0<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "So y = -2<BR>\n" );
document.write( "z = 5<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Check each original eqn:<BR>\n" );
document.write( "2x + y = -2<BR>\n" );
document.write( "-x + 3y - 4z = -26<BR>\n" );
document.write( "5x - 6y + z = 17 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The 1st is good.<BR>\n" );
document.write( "0 + 3(-2) - 4*5 = -26  is good.<BR>\n" );
document.write( "0 -6(-2) + 5 = 17 is good.<BR>\n" );
document.write( "It all works.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "I think doing eliminating 1 variable at a time works better.  Other methods might work, too, as you tried, but it's more confusing.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );