document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121327>Question 1121327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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\r<BR>\n" );
document.write( "\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.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737174 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (i) No solution.<BR>\n" );
document.write( "Parallel lines have the same slope, but not the same y-intercept<BR>\n" );
document.write( "Express the equations in standard form:<BR>\n" );
document.write( "y = (-9/k)x + 3/k<BR>\n" );
document.write( "y = -kx + 1<BR>\n" );
document.write( "m1 = -9/k, m2 = -k<BR>\n" );
document.write( "m1 = m2 -> -9/k = -k -> k^2 = 9<BR>\n" );
document.write( "This gives k = 3, k = -3<BR>\n" );
document.write( "k = -3 will result in a different y-intercept<BR>\n" );
document.write( "The two equations are <BR>\n" );
document.write( "y = 3x - 3<BR>\n" );
document.write( "y = 3x + 1<BR>\n" );
document.write( "(ii) Using the results from (i), when k = 3, the two equations are the same:<BR>\n" );
document.write( "y = -3x + 1<BR>\n" );
document.write( "y = -3x + 1<BR>\n" );
document.write( "(iii) Any value other than k = 3, k = -3, will result in one intersection point, or one solution<BR>\n" );
document.write( "For example, if k = 1 we have<BR>\n" );
document.write( "y = -9x + 3<BR>\n" );
document.write( "y = -x + 1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );