document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=603886>Question 603886</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me solve the equations ax + by = m  and cx + dy = n.  somehow the answer is supposed to be those two equations combined into one.  \r<BR>\n" );
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document.write( "I need an answer asap\r<BR>\n" );
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document.write( "everything I have done is wrong and I need to know how to figure them out.<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 #380866 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=380866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can you help me solve the equations ax + by = m  and cx + dy = n.<BR>\n" );
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document.write( "Use determinants\r<BR>\n" );
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document.write( "|a b -m|<BR>\n" );
document.write( "|c d -n|<BR>\n" );
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document.write( "Det = ab - cd<BR>\n" );
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document.write( "x*Det = b*-n - d*-m = dm - bn<BR>\n" );
document.write( "-y*Det = a*-n - c*-m = cm - an<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "x = (dm - bn)/(ab - cd)<BR>\n" );
document.write( "y = (an - cm)/(ab - cd)<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Without determinants:<BR>\n" );
document.write( "ax + by = m Eqn 1<BR>\n" );
document.write( "cx + dy = n Eqn 2<BR>\n" );
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document.write( "acx + bcy = cm Eqn 1 times c<BR>\n" );
document.write( "acx + ady = an Eqn 2 times a<BR>\n" );
document.write( "------------------------ Subtract<BR>\n" );
document.write( "y*(bc-ad) = cm - an<BR>\n" );
document.write( "y = (an - cm)/(ad - bc)  (I flipped both NUM and DEN)<BR>\n" );
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document.write( "ax + by = m Eqn 1<BR>\n" );
document.write( "cx + dy = n Eqn 2<BR>\n" );
document.write( "------<BR>\n" );
document.write( "adx + bdy = dm Eqn 1 times d<BR>\n" );
document.write( "bcx + bdy = bn Eqn 2 times b<BR>\n" );
document.write( "------------------------ Subtract<BR>\n" );
document.write( "x*(ad - bc) = dm - bn<BR>\n" );
document.write( "x = (dm - bn)/(ad - bc)\r<BR>\n" );
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