document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=676683>Question 676683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with this question? I need it answer by today.\r<BR>\n" );
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document.write( "For what values of k is the system of equations independent?\r<BR>\n" );
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document.write( "4x + y	 = 	4<BR>\n" );
document.write( "kx + y	 = 	6\r<BR>\n" );
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document.write( "Write the first equation in slope-intercept form. Subtract <BR>\n" );
document.write( "4x<BR>\n" );
document.write( " from each side of the equation<BR>\n" );
document.write( "4x + y = 4.<BR>\n" );
document.write( "y =   + 4\r<BR>\n" );
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document.write( "art (b)<BR>\n" );
document.write( "x + 2y	 = 	5<BR>\n" );
document.write( "kx + 3y	 = 	3\r<BR>\n" );
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document.write( "Part (c)<BR>\n" );
document.write( "2x + ky	 = 	7<BR>\n" );
document.write( "x + 2y	 = 	4\r<BR>\n" );
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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 #420457 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=420457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For what values of k is the system of equations independent? <BR>\n" );
document.write( "4x + y = 4<BR>\n" );
document.write( "kx + y = 6<BR>\n" );
document.write( "The 2 eqns are independent for all values of k.<BR>\n" );
document.write( "If k = 4, they're inconsistent.<BR>\n" );
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document.write( "Write the first equation in slope-intercept form. <BR>\n" );
document.write( "Subtract 4x<BR>\n" );
document.write( "from each side of the equation<BR>\n" );
document.write( "4x + y = 4.<BR>\n" );
document.write( "y = + 4 ***************** y = 4 - 4x<BR>\n" );
document.write( "Or y = -4x + 4 is the form y = mx + b<BR>\n" );
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document.write( "art (b)<BR>\n" );
document.write( "x + 2y = 5<BR>\n" );
document.write( "kx + 3y = 3<BR>\n" );
document.write( "Same as the 1st question, but<BR>\n" );
document.write( "if k = 1.5 the eqns are inconsistent.<BR>\n" );
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document.write( "x + 2y = 5<BR>\n" );
document.write( "2y = -x + 5<BR>\n" );
document.write( "y = (-1/2)x + 5/2 <BR>\n" );
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document.write( "Part (c)<BR>\n" );
document.write( "2x + ky = 7<BR>\n" );
document.write( "x + 2y = 4 <BR>\n" );
document.write( "Same, if k = 4 --> inconsistent<BR>\n" );
document.write( "2x + ky = 7<BR>\n" );
document.write( "ky = -2x + 7<BR>\n" );
document.write( "y = (-2/k)x + 7/k </SPAN>\n" );
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