document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30328>Question 30328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> AX+BY=P<BR>\n" );
document.write( "BX-AY=Q SOLVE FORX&Y<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 #17003 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=17003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> AX+BY=P ----(1)multiplied by A<BR>\n" );
document.write( "BX-AY=Q ----(2)multiplied by B\r<BR>\n" );
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document.write( "(1) is multiplied by A and (2) is multiplied by B <BR>\n" );
document.write( "so that the coefficients of Y are made the same.\r<BR>\n" );
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document.write( "A^2X +(AB)Y = AP ----(3)<BR>\n" );
document.write( "B^2X -(AB)Y = BQ ----(4)<BR>\n" );
document.write( "(3) + (4) gives<BR>\n" );
document.write( "(A^2+B^2)X = AP+BQ <BR>\n" );
document.write( "Dividing by (A^2+B^2)<BR>\n" );
document.write( "X = (AP+BQ)/(A^2+B^2) ----(*)<BR>\n" );
document.write( "Putting (*) in (1)<BR>\n" );
document.write( "AX+BY =P<BR>\n" );
document.write( "A times[(AP+BQ)/(A^2+B^2)]+BY = P<BR>\n" );
document.write( "Multiplying by (A^2+B^2)<BR>\n" );
document.write( "A(AP+BQ) +B(A^2+B^2)Y = P(A^2+B^2)<BR>\n" );
document.write( "B(A^2+B^2)Y = P(A^2+B^2)-A(AP+BQ)<BR>\n" );
document.write( "B(A^2+B^2)Y = PA^2+PB^2-PA^2-ABQ <BR>\n" );
document.write( "B(A^2+B^2)Y = (PA^2-PA^2)+PB^2-ABQ<BR>\n" );
document.write( "B(A^2+B^2)Y = (PA^2-PA^2)+PB^2-ABQ <BR>\n" );
document.write( "B(A^2+B^2)Y = 0+B(BP-AQ)<BR>\n" );
document.write( "B(A^2+B^2)Y = B(BP-AQ)<BR>\n" );
document.write( "Dividing by B(A^2+B^2)<BR>\n" );
document.write( "Y = (BP-AQ)/(A^2+B^2)<BR>\n" );
document.write( "Answer: X = (AP+BQ)/(A^2+B^2)  and Y = (BP-AQ)/(A^2+B^2)<BR>\n" );
document.write( "Note:Instead of substituting for X and getting Y,we may give a similar treatment of equalising coefficients and using subtractilon to get rid of X to get Y.<BR>\n" );
document.write( "Verification:Since (1) was used to find Y substituting for X we shall <BR>\n" );
document.write( "use (2) for verification.<BR>\n" );
document.write( "BX-AY=Q ----(2)<BR>\n" );
document.write( "Putting X = (AP+BQ)/(A^2+B^2)  and Y = (BP-AQ)/(A^2+B^2)in this<BR>\n" );
document.write( "LHS = B(AP+BQ)/(A^2+B^2)  - A(BP-AQ)/(A^2+B^2)<BR>\n" );
document.write( "=[1/(A^2+B^2)]multiplied by[B(AP+BQ)- A(BP-AQ)]<BR>\n" );
document.write( "=[1/(A^2+B^2)]multiplied by(ABP+B^2Q-ABP+A^2Q]<BR>\n" );
document.write( "=(ABP-ABP+A^2Q+B^2Q]/(A^2+B^2)<BR>\n" );
document.write( "=[0+(A^2+B^2)Q]/(A^2+B^2)<BR>\n" );
document.write( "=(A^2+B^2)Q]/(A^2+B^2)<BR>\n" );
document.write( "=Q (cancelling (A^2+B^2)<BR>\n" );
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