document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251662>Question 251662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ax+by=u<BR>\n" );
document.write( "cx+d y=v  when d is=[a b c d]=/0 what is the answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184425 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=184425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think I understand your question. Let's first solve for x and y in terms of a, b, c, d, u, and v.<BR>\n" );
document.write( "multiply the first equation by c and the second equation by -a:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%28ax+%2B+by+=+u%29 ALIGN=MIDDLE  ALT=\"c%28ax+%2B+by+=+u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%28cx+%2B+dy+=+v%29 ALIGN=MIDDLE  ALT=\"-a%28cx+%2B+dy+=+v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This will eliminate the x variable and we can solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cby+-+ady+=+cu+-+av ALIGN=MIDDLE  ALT=\"cby+-+ady+=+cu+-+av\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, y equals<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28cu+-+av%29+%2F+%28bc+-+ad%29 ALIGN=MIDDLE  ALT=\"+y+=+%28cu+-+av%29+%2F+%28bc+-+ad%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting that into the first equation for x, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax+%2B+b%28cu+-+av%29%2F%28bc-ad%29+=+u ALIGN=MIDDLE  ALT=\"ax+%2B+b%28cu+-+av%29%2F%28bc-ad%29+=+u\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for x, we get<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ad%29%29%29%2Fa ALIGN=MIDDLE  ALT=\"X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ad%29%29%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have solve for X and Y in terms of a, b, c, d, u, and v. <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Case 1: let d = a.<BR>\n" );
document.write( "From (i and ii) we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-a%5E2%29%29%29%2Fa ALIGN=MIDDLE  ALT=\"X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-a%5E2%29%29%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28cu+-+av%29+%2F+%28bc+-+a%5E2%29 ALIGN=MIDDLE  ALT=\"+y+=+%28cu+-+av%29+%2F+%28bc+-+a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "case 2: let d = b.<BR>\n" );
document.write( "From (i and ii) we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ab%29%29%29%2Fa ALIGN=MIDDLE  ALT=\"X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ab%29%29%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > - -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+%28u+-+%28%28cu+-+av%29%2F%28c-a%29%29%29%2Fa ALIGN=MIDDLE  ALT=\"X+=+%28u+-+%28%28cu+-+av%29%2F%28c-a%29%29%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28cu+-+av%29+%2F+%28bc+-+ab%29 ALIGN=MIDDLE  ALT=\"+y+=+%28cu+-+av%29+%2F+%28bc+-+ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "case 3: d = c.<BR>\n" );
document.write( "From (i and ii) we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ac%29%29%29%2Fa ALIGN=MIDDLE  ALT=\"X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ac%29%29%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28cu+-+av%29+%2F+%28bc+-+ac%29 ALIGN=MIDDLE  ALT=\"+y+=+%28cu+-+av%29+%2F+%28bc+-+ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "case 4: d = d<BR>\n" );
document.write( "From (i and ii) we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ad%29%29%29%2Fa ALIGN=MIDDLE  ALT=\"X+=+%28u+-+b%28%28cu+-+av%29%2F%28bc-ad%29%29%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28cu+-+av%29+%2F+%28bc+-+ad%29 ALIGN=MIDDLE  ALT=\"+y+=+%28cu+-+av%29+%2F+%28bc+-+ad%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "I hope that helps and is what you were looking for.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );