document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=354768>Question 354768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To buy both a new car and a new house, Tina sought two loans totalling $78,825. The simple interest rate on the first loan was 0.2%, while the simple interest rate on the second loan was 5.0%. At the end of the first year, Tina paid a combined interest payment of $2817.23. What were the amounts of the two loans?\r<BR>\n" );
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document.write( "So far I have this but don't know where to go from there:<BR>\n" );
document.write( "x + y = 78,825<BR>\n" );
document.write( "0.02x + 0.05y = 2817.23 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #253468 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=253468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Typo or error?  Your problem statement says the first loan is at 0.2% simple interest, which really looks like a typo, but if 0.2% is actually correct, then your second equation has an error and should be:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0.002x\ +\ 0.05y\ =\ 2817.23\">\r<BR>\n" );
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document.write( "Either way, there are three basic ways to go about solving your system:\r<BR>\n" );
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document.write( "1.  Substitution:\r<BR>\n" );
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document.write( "Solve <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ y\ =\ 78825\"> for either of the variables in terms of the other.  Let's solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 78825\ -\ x\">\r<BR>\n" );
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document.write( "Now substitute into the 2nd equation.  (I'm going to go with my gut feeling and say you had a typo in the problem statement, but you can make the adjustment if necessary)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 0.02x\ +\ 0.05(78825\ -\ x)\ =\ 2817.23\">\r<BR>\n" );
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document.write( "And then just solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.\r<BR>\n" );
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document.write( "2.  Elimination:\r<BR>\n" );
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document.write( "Multiply your second equation by -50:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -50(0.02x\ +\ 0.05y)\ =\ -50(2817.23)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -x\ -\ 2.5y\ =\ -148861.5\">\r<BR>\n" );
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document.write( "Then add the two equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ (-x)\ +\ y\ +\ (-2.5)y\ =\ 78825\ -\ 148861.5\">\r<BR>\n" );
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document.write( "Notice that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> goes away leaving you with an equation in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">\r<BR>\n" );
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document.write( "3. Cramer's Rule:\r<BR>\n" );
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document.write( "Create the coefficient matrix of your system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ \ \ \ 1\ \ \ \ \ 1\cr 0.02\ 0.05\right\]\">\r<BR>\n" );
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document.write( "And then calculate the determinant, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large D\">, of that matrix.\r<BR>\n" );
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document.write( "The determinant\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left|a_1\ b_1\cr a_2\ b_2\right|\ =\ a_1b_2\ -\ a_2b_1\">\r<BR>\n" );
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document.write( "So you will have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left|\ \ \ \ 1\ \ \ \ \ 1\cr 0.02\ 0.05\right|\ =\ 0.05\ -\ 0.02\ =\ 0.03\">\r<BR>\n" );
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document.write( "Then replace the first column of your matrix with the constant values from your equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ \ 78825\ \ \ \ \ 1\cr 2817.23\ 0.05\right\]\">\r<BR>\n" );
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document.write( "and then using the same process, calculate the determinant, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large D_x\">\r<BR>\n" );
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document.write( "Next, replace the second column:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left\[\ \ \ \ 1\ \ \,78825\cr 0.02\ 2817.23\right\]\">\r<BR>\n" );
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document.write( "From which you calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large D_y\">\r<BR>\n" );
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document.write( "Finally,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{D_x}{D}\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{D_y}{D}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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