document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=52885>Question 52885</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations: (hint: let (1/x)=t and (1/y)=u)\r<BR>\n" );
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document.write( "(2/x)+(1/y)=11<BR>\n" );
document.write( "(3/x)-(5/y)=10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35267 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=35267\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (2/x)+(1/y)=11<BR>\n" );
document.write( "(3/x)-(5/y)=10<BR>\n" );
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document.write( "2(1/x)+(1/y)=11<BR>\n" );
document.write( "3(1/x)-5(1/y)=10<BR>\n" );
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document.write( "Let 1/x=t and 1/y=u<BR>\n" );
document.write( "2t+u=11<BR>\n" );
document.write( "3t-5u=10<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Solve the first equation for u, substitute it for u in the second equation and solve for t.<BR>\n" );
document.write( "2t+u=11<BR>\n" );
document.write( "-2t+2t+u=-2t+11<BR>\n" );
document.write( "u=-2t+11<BR>\n" );
document.write( "3t-5(-2t+11)=10<BR>\n" );
document.write( "3t+10t-55=10<BR>\n" );
document.write( "13t-55=10<BR>\n" );
document.write( "13t-55+55=10+55<BR>\n" );
document.write( "13t=65<BR>\n" );
document.write( "13t/13=65/13<BR>\n" );
document.write( "t=5<BR>\n" );
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document.write( "Substitute that answer for t in the first equation and solve for u.<BR>\n" );
document.write( "2(5)+u=11<BR>\n" );
document.write( "10+u=11<BR>\n" );
document.write( "-10+10+u=11-10<BR>\n" );
document.write( "u=1<BR>\n" );
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document.write( "Only we were supposed to find x and y not t and u, so let t=1/x and u=1/y and solve for x and y.<BR>\n" );
document.write( "t=5 becomes 1/x=5<BR>\n" );
document.write( "x(1/x)=5x<BR>\n" );
document.write( "1=5x<BR>\n" );
document.write( "1/5=5x/5<BR>\n" );
document.write( "1/5=x<BR>\n" );
document.write( "u=1 becomes 1/y=1<BR>\n" );
document.write( "y(1/y)=1(y)<BR>\n" );
document.write( "1=y<BR>\n" );
document.write( "Therefore, our answer is (x,y)=(1/5,1) </SPAN>\n" );
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