document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360274>Question 360274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x + 3y + 3z = 6<BR>\n" );
document.write( "-x + y + z = 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257114 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=257114\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Multiply the bottom equation by 2.  <BR>\n" );
document.write( "-2x+2y+2z = 4.  Add corresponding sides with the top equation, to get<BR>\n" );
document.write( "5y +5z = 10, or y+z = 2.  Substitute this into the bottom equation:<BR>\n" );
document.write( "-x + (2-z) +z = 2, or -x+2 = 2, or -x = 0, or x = 0. However, y is still y = 2-z, and so the system is dependent, or has infinitely-many ordered triples as solution.  The solution set is the set of all triples (0,2-z,z), where z is any real number. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );