document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076487>Question 1076487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the following: 2/3x+y=16 and kx+3y=48\r<BR>\n" );
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document.write( "For what values of k does the linear system below have:<BR>\n" );
document.write( "a) infinite solutions?<BR>\n" );
document.write( "b) one solution?<BR>\n" );
document.write( "c) no solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691095 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=691095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (2/3)x+y=16<BR>\n" );
document.write( "kx+3y=48<BR>\n" );
document.write( "if kx=2, then 2x+3y=48 and multiplying the top by 3, 2x+3y=48, the same.<BR>\n" );
document.write( "Therefore k=2 for infinite solutions.<BR>\n" );
document.write( "The slope of the first is -2/3, and slope intercept form is -2x/3+16<BR>\n" );
document.write( "the slope of the second is -(1/3)k and slope intercept form is -k/3+16<BR>\n" );
document.write( "For k equal to any other number than 2, there will be one point of intersection.  <BR>\n" );
document.write( "For no solution, the two lines have to be parallel, and the line kx+3y=48 becomes 3y=-kx+48 and <BR>\n" );
document.write( "y=-(k/3)+16.  The y-intercept doesn't change with k, so there is no value where the lines are parallel without being the same line. </SPAN>\n" );
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