document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32119>Question 32119</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of k for which the system of linear equations 2x+5y=3 ; (k+1)x+2(k+2)y=2k will have infinite number of solutions . ( Pls answer . .. Its urget ..........THAnkS<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 #18634 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For there to be an infinite number of solutions, the<BR>\n" );
document.write( "equation (k+1)x+2(k+2)y=2k must be a multiple of <BR>\n" );
document.write( "the equation 2x+5y=3<BR>\n" );
document.write( "Let the multiplier by \"a\".<BR>\n" );
document.write( "Then the equation is 2ax+5ay=3a<BR>\n" );
document.write( "Then the following set of equation must be true:<BR>\n" );
document.write( "k+1=2a<BR>\n" );
document.write( "2k=3a<BR>\n" );
document.write( "Then k=3a/2<BR>\n" );
document.write( "Substitute that into k+1=2a to get:<BR>\n" );
document.write( "(3a/2)+1=2a<BR>\n" );
document.write( "(1/2)a=1<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "If a=2 then 2k=3(2) and k=3<BR>\n" );
document.write( "Try It:<BR>\n" );
document.write( "Substituting for \"k\" you get:<BR>\n" );
document.write( "(3+1)x+2(3+2)y=2(3)<BR>\n" );
document.write( "4x+10y=6<BR>\n" );
document.write( "This is a multiple of the equation 2x+5y=3 <BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );