document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87234>Question 87234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me on how to do this problem:<BR>\n" );
document.write( " Determine the constant k so that ( -2,3) will satisfy the equation - kx-4y= -k<BR>\n" );
document.write( " PLEASE HELP ME!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63182 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=63182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "-kx - 4y= -k<BR>\n" );
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document.write( "This equation must be true for the point (-2, 3) which means it must be hold true when<BR>\n" );
document.write( "x is -2 and y is +3.<BR>\n" );
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document.write( "Substitute those values in for x and y to get:<BR>\n" );
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document.write( "-k(-2) -4(+3) = -k<BR>\n" );
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document.write( "Multiply out the two terms on the left to get:<BR>\n" );
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document.write( "+2k - 12 = -k<BR>\n" );
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document.write( "Next, we need to get the terms containing k on one side of the equation and everything<BR>\n" );
document.write( "else on the other side.  We can get rid of the -k on the right side by adding +k to both <BR>\n" );
document.write( "sides.  On the right side the addition of -k and +k results in zero. And on the left side<BR>\n" );
document.write( "the +k adds to the +2k.  This results in:<BR>\n" );
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document.write( "3k - 12 = 0<BR>\n" );
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document.write( "Next add 12 to both sides to get rid of the -12 on the left side. With this addition<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
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document.write( "3k = 12<BR>\n" );
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document.write( "Solve for k by dividing both sides by 3 ... the multiplier of k.  The result of this<BR>\n" );
document.write( "division give us the value of k as:<BR>\n" );
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document.write( "k = 12/3 = 4<BR>\n" );
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document.write( "check the answer by substituting 4 for k in the original given equation.  When you do,<BR>\n" );
document.write( "the equation:<BR>\n" );
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document.write( "-kx - 4y= -k<BR>\n" );
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document.write( "becomes:<BR>\n" );
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document.write( "-4x -4y = -4<BR>\n" );
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document.write( "Divide all terms by -4 to get:<BR>\n" );
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document.write( "x + y = 1<BR>\n" );
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document.write( "Does (-2, 3) satisfy this equation? Substitute -2 for x and +3 for y to get:<BR>\n" );
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document.write( "-2 + 3 = 1<BR>\n" );
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document.write( "Add the terms on the left side and you get:<BR>\n" );
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document.write( "1 = 1<BR>\n" );
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document.write( "This verifies that k = 4 because it works in the equation and (-2, 3) is a solution<BR>\n" );
document.write( "when k has this value.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.\r<BR>\n" );
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