document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84282>Question 84282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When working with several different equations as a system such as below:\r<BR>\n" );
document.write( "\n" );
document.write( "2X - Y + 4Z = -5<BR>\n" );
document.write( "X + 2Y - Z = 6<BR>\n" );
document.write( "X + Y + Z = 1\r<BR>\n" );
document.write( "\n" );
document.write( "How many solutions are there ( none, 1, 3, or infinite) Please explain.\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks, I am a 48 year old male returning to college math after almost 30 years and am very confused right now...\r<BR>\n" );
document.write( "\n" );
document.write( "Keith </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60684 by </B><A HREF=/tutors/aboutme.mpl?userid=checkley75><B>checkley75(3666)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=checkley75><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THERE SHOULD BE 3 TOTAL SOLUTION: 1 FOR X, 1 FOR Y & 1 FOR Z.<BR>\n" );
document.write( "X+Y+Z=1<BR>\n" );
document.write( "X+2Y-Z=6 NOW ADD THESE TWO EQUATIONS THUS:<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "2X+3Y=7 NOW SUBTRACT THE FIRST EAUATION<BR>\n" );
document.write( "-(2X-Y+4Z=-5)<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "4Y+4Z=12 REDUCING THIS EQUATIONWE GET:<BR>\n" );
document.write( "Y+Z=3 NIOW SUBSTITUTE 3 FOR (Y=Z) IN THE THIRD EQUATION THUS:<BR>\n" );
document.write( "X+3=1<BR>\n" );
document.write( "X=1-3<BR>\n" );
document.write( "X=-2 ANSWER. NOW SUBSTITUTE -2 FOR X IN THE EQUATION 2X+3Y=7 & SOLVE FOR Y:<BR>\n" );
document.write( "2*-2+3Y=7<BR>\n" );
document.write( "-4+3Y=7<BR>\n" );
document.write( "3Y=7+4<BR>\n" );
document.write( "3Y=11<BR>\n" );
document.write( "Y=11/3 ANSWER. <BR>\n" );
document.write( "-2+11/3+Z=1<BR>\n" );
document.write( "Z=1+2-11/3<BR>\n" );
document.write( "Z=3-11/3<BR>\n" );
document.write( "Z=(9-11)/3<BR>\n" );
document.write( "Z=-2/3 ANSWER.<BR>\n" );
document.write( "-------------------------------------------------------------------------------<BR>\n" );
document.write( "I'LL LEAVE THE PROOF UP TO YOU. IT'S GOOD PRACTICE TO SOLVE ALL THREE EQUATIONS.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );