document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62306>Question 62306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble solving these systems.  I get lost somewhere in the middle and it becomes a mess. Please help.<BR>\n" );
document.write( "x-2y-3z=4<BR>\n" );
document.write( "2x-4y+5z=-3<BR>\n" );
document.write( "5x-6y+4z=-7\r<BR>\n" );
document.write( "\n" );
document.write( "and\r<BR>\n" );
document.write( "\n" );
document.write( "2x-y=-1<BR>\n" );
document.write( "-2x+z=1<BR>\n" );
document.write( "y-z=0\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 #43202 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=43202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve:<BR>\n" );
document.write( "(1)  x-2y-3z=4<BR>\n" );
document.write( "(2)  2x-4y+5z=-3<BR>\n" );
document.write( "(3)  5x-6y+4z=-7\r<BR>\n" );
document.write( "\n" );
document.write( "First, I will state the operations that we are allowed to perform on these equations without changing the solutions:<BR>\n" );
document.write( "(a) We can interchange any two equations<BR>\n" );
document.write( "(b) We can multiply an equation by a constant other than zero<BR>\n" );
document.write( "(c) We can multiply an equation by a constant other than zero and add it to another equation, replacing that equation\r<BR>\n" );
document.write( "\n" );
document.write( "We'll start by doing (c).  We'll multiply equation (1) by -2 and then add equation (1) to equation (2) and we will get:\r<BR>\n" );
document.write( "\n" );
document.write( "(1) -2x+4y+6z=-8<BR>\n" );
document.write( "(2)  0x+0y+11z=-11 from this equation, we see that z=-1<BR>\n" );
document.write( "(3)  5x-6y+4z=-7\r<BR>\n" );
document.write( "\n" );
document.write( "Next, we'll plug z=-1 into eq (1) and (3) and get:\r<BR>\n" );
document.write( "\n" );
document.write( "(1)  -2x+4y=-2 <BR>\n" );
document.write( "(3)   5x-6y=-3\r<BR>\n" );
document.write( "\n" );
document.write( "Next, we'll multiply eq (1) by 5 and eq (3) by 2 and we get:\r<BR>\n" );
document.write( "\n" );
document.write( "(1)  -10x+20y=-10<BR>\n" );
document.write( "(3)   10x-12y=-6\r<BR>\n" );
document.write( "\n" );
document.write( "Now add eq (1) to eq (3), replacing eq (3) and we have:\r<BR>\n" );
document.write( "\n" );
document.write( "(1)  -10x+20y=-10<BR>\n" );
document.write( "(3)    0x+ 8y=-16  and here we have y=-2\r<BR>\n" );
document.write( "\n" );
document.write( "Next divide eq (1) by -10 <BR>\n" );
document.write( "(1)  x-2y=1  now plug in y=-2 and we have:<BR>\n" );
document.write( "(1)  x+4=1 ;x=-3<BR>\n" );
document.write( "We now have <BR>\n" );
document.write( "x=-3<BR>\n" );
document.write( "y=-2<BR>\n" );
document.write( "z=-1\r<BR>\n" );
document.write( "\n" );
document.write( "I'll leave the second problem up to you.  It looks to be fairly straightforward.  Hint: You know from eq (3) that y=z.  What happens if you plug that into equation (1), then add eq (1) and (2)?\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps----ptaylor\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );