document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198864>Question 1198864</A>: <I><SPAN STYLE=\"word-break: break-all;\">  For what value of k does the following system have infinitely many solutions?<BR>\n" );
document.write( "kx + y + z=0<BR>\n" );
document.write( "x + 2y + kz = 0<BR>\n" );
document.write( "-X+3z=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832522 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Solve the 3rd equation for z and substitute in the other two equations.<br><BR>\n" );
document.write( "x = 3z<br><BR>\n" );
document.write( "3kz+y+z=0<BR>\n" );
document.write( "3z+2y+kz=0<br><BR>\n" );
document.write( "y+(3k+1)z=0<BR>\n" );
document.write( "2y+(3+k)z=0<br><BR>\n" );
document.write( "There are infinitely many solutions if the two equations are equivalent.<br><BR>\n" );
document.write( "2y+(6k+2)z=0<BR>\n" );
document.write( "2y+(3+k)z=0<br><BR>\n" );
document.write( "6k+2=3+k<BR>\n" );
document.write( "5k=1<BR>\n" );
document.write( "k=1/5<br><BR>\n" );
document.write( "ANSWER: k=1/5<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );