document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=676784>Question 676784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with this problem?\r<BR>\n" );
document.write( "\n" );
document.write( "x + 2y	 = 	5<BR>\n" );
document.write( "kx + 3y	 = 	3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For the system to be independent the slopes must not be the same. Study the two equations and complete the following inequality for the slopes.<BR>\n" );
document.write( "&#8722; k/3=\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply both sides by &#8722;3.<BR>\n" );
document.write( "k &#8800;  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420607 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><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=420607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + 2y = 5<BR>\n" );
document.write( "rearranged as<BR>\n" );
document.write( "2y = -x + 5<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F2%29x+%2B+%285%2F2%29 ALIGN=MIDDLE  ALT=\"%28-1%2F2%29x+%2B+%285%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> linear equation for this line<BR>\n" );
document.write( "...<BR>\n" );
document.write( "kx + 3y = 3<BR>\n" );
document.write( "rearranged as<BR>\n" );
document.write( "3y = -kx + 3<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-k%2F3%29x+%2B+%283%2F3%29 ALIGN=MIDDLE  ALT=\"%28-k%2F3%29x+%2B+%283%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> linear equation for this line<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Since the slopes cannot be the same, solve for k when they are set equal<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F2%29=%28-k%2F3%29 ALIGN=MIDDLE  ALT=\"%28-1%2F2%29=%28-k%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "-3 = -2k<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the slopes are the same.<BR>\n" );
document.write( "therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C%3E3%2F2 ALIGN=MIDDLE  ALT=\"k%3C%3E3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".....................<BR>\n" );
document.write( "Delighted to help.<BR>\n" );
document.write( "-Reading Boosters<BR>\n" );
document.write( "Website: www.MyHomeworkAnswers.com <BR>\n" );
document.write( "Wanting for others what we want for ourselves. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );