document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121330>Question 1121330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question.\r<BR>\n" );
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document.write( "Find the value(s) of the constant k such that the system of linear equations:<BR>\n" );
document.write( "9x + ky = 3,<BR>\n" );
document.write( "kx + y = 1<BR>\n" );
document.write( "has<BR>\n" );
document.write( "(i) No solution.<BR>\n" );
document.write( "(ii) An infinite number of solutions.<BR>\n" );
document.write( "(iii) Exactly one solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737166 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> write in slope-intercept form<BR>\n" );
document.write( "the first is ky=-9x+3 or y=-(9/k)x+(3/k)<BR>\n" );
document.write( "the second is y=-kx+1<BR>\n" );
document.write( "The slopes are (-9/k) and -k.  <BR>\n" );
document.write( "For no or infinite solutions, the slopes are equal so set -9/k=-k<BR>\n" );
document.write( "-k^2=-9<BR>\n" );
document.write( "k=3 or -3<BR>\n" );
document.write( "y=-3k+1<BR>\n" );
document.write( "y=-3k+1<BR>\n" );
document.write( "So for k=3, there are infinite solutions\r<BR>\n" );
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document.write( "try k=-3<BR>\n" );
document.write( "y=3x-1<BR>\n" );
document.write( "y=3x+1, there are no solutions (parallel lines)<BR>\n" );
document.write( "For all other k, there is one solution.<BR>\n" );
document.write( " </SPAN>\n" );
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