document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=576307>Question 576307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having problems with this.\r<BR>\n" );
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document.write( "Use Cramer's rule to solve the<BR>\n" );
document.write( "following system of equations.<BR>\n" );
document.write( "If D = 0, use another method<BR>\n" );
document.write( "to solve. <BR>\n" );
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document.write( "2x/3-5y/2=3/2<BR>\n" );
document.write( "-x/4+5y/2=7/2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369796 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=369796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "For the matrix\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]\">\r<BR>\n" );
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document.write( "The determinant is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ D\ =\ \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( "Given the system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left\{a_1x\ +\ b_1y\ =\ c_1\cr a_2x\ +\ b_2y\ =\ c_2\right\">\r<BR>\n" );
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document.write( "First calculate the determinant of the coefficient matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ D\ =\ \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( "Then replace the first column with the constant values and calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE D_x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ D_x\ =\ \left|c_1\ \ b_1\cr c_2\ \ b_2\right|\ =\ c_1b_2\ -\ c_2b_1\">\r<BR>\n" );
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document.write( "Then replace the second column with the constant values and calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE D_y\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ D_y\ =\ \left|a_1\ \ c_1\cr a_2\ \ c_2\right|\ =\ a_1c_2\ -\ a_2c_1\">\r<BR>\n" );
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document.write( "Finally, solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ =\ \frac{D_x}{D}\"> and <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( "For your problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ D\ =\ \left(\frac{2}{3}\right)\left(\frac{5}{2}\right)\ -\ \left(-\frac{1}{4}\right)\left(-\frac{5}{2}\right)\ =\ \frac{5}{3}\ -\ \frac{5}{8}\ =\ \frac{25}{24}\">\r<BR>\n" );
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document.write( "I'll let you do the rest of the arithmetic.\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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