document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090975>Question 1090975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me here.<BR>\n" );
document.write( "Ax+By=C<BR>\n" );
document.write( "Dx+Ey=F<BR>\n" );
document.write( "Solve the system for x and y <BR>\n" );
document.write( "I got x=C-By/A<BR>\n" );
document.write( "y= (AF-CD)/(AE-BD)<BR>\n" );
document.write( "Not sure if I am right. <BR>\n" );
document.write( "Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705414 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=705414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "You can use <a  rel=nofollow HREF=\"http://www.coolmath.com/algebra/14-determinants-cramers-rule/01-determinants-cramers-rule-2x2-01\">Cramer's Rule</a> to solve this. Let's define the following\r<BR>\n" );
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document.write( "<li>P = the matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2CA%2CB%2CD%2CE%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2CA%2CB%2CD%2CE%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice it's the left hand side coefficients)</li><BR>\n" );
document.write( "<li>Px = the matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2CC%2CB%2CF%2CE%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2CC%2CB%2CF%2CE%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I started with matrix P and I've replaced the first column with C and F, both of which are the right hand side values</li><BR>\n" );
document.write( "<li>Py = the matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2CA%2CC%2CD%2CF%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2CA%2CC%2CD%2CF%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I started with matrix P ann replaced the second column with C and F, both of which are the right hand side values</li><BR>\n" );
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document.write( "The notation det(P) is the determinant of matrix P. Using the <a  rel=nofollow HREF=\"http://www.purplemath.com/modules/determs.htm\">two-by-two matrix determinant rule</a> we can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=det%28P%29+=+A%2AE+-+B%2AD ALIGN=MIDDLE  ALT=\"det%28P%29+=+A%2AE+-+B%2AD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=det%28Px%29+=+C%2AE+-+F%2AB ALIGN=MIDDLE  ALT=\"det%28Px%29+=+C%2AE+-+F%2AB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=det%28Px%29+=+A%2AF+-+C%2AD ALIGN=MIDDLE  ALT=\"det%28Px%29+=+A%2AF+-+C%2AD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then you divide the determinants to get x and y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28det%28Px%29%29%2F%28det%28P%29%29+=+%28C%2AE+-+F%2AB%29%2F%28A%2AE+-+B%2AD%29 ALIGN=MIDDLE  ALT=\"x+=+%28det%28Px%29%29%2F%28det%28P%29%29+=+%28C%2AE+-+F%2AB%29%2F%28A%2AE+-+B%2AD%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28det%28Px%29%29%2F%28det%28P%29%29+=+%28A%2AF+-+C%2AD%29%2F%28A%2AE+-+B%2AD%29 ALIGN=MIDDLE  ALT=\"y+=+%28det%28Px%29%29%2F%28det%28P%29%29+=+%28A%2AF+-+C%2AD%29%2F%28A%2AE+-+B%2AD%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we knew the values of A,B,C,D,E, and F, then we could compute the actual numeric values of x and y. However, since we don't know those six variables, we just leave it as shown above. \r<BR>\n" );
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document.write( "So the final answers are <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28C%2AE+-+F%2AB%29%2F%28A%2AE+-+B%2AD%29 ALIGN=MIDDLE  ALT=\"x+=+%28C%2AE+-+F%2AB%29%2F%28A%2AE+-+B%2AD%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28A%2AF+-+C%2AD%29%2F%28A%2AE+-+B%2AD%29 ALIGN=MIDDLE  ALT=\"y+=+%28A%2AF+-+C%2AD%29%2F%28A%2AE+-+B%2AD%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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