document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=386442>Question 386442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The line 3x + 4y = 15 intersects the curve 2xy = 9 at A and B. Find <BR>\n" );
document.write( "a) the coordinates of A and of B, <BR>\n" );
document.write( "b) the distance AB </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #273191 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=273191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The line 3x + 4y = 15 intersects the curve 2xy = 9 at A and B. Find <BR>\n" );
document.write( "a) the coordinates of A and of B, <BR>\n" );
document.write( "b) the distance AB<BR>\n" );
document.write( "...<BR>\n" );
document.write( "3x+4y=15<BR>\n" );
document.write( "2xy=9<BR>\n" );
document.write( "y= 9/2x<BR>\n" );
document.write( "substitute the value of y in first equation<BR>\n" );
document.write( "3x+4y=15<BR>\n" );
document.write( "3x+4*(9/2x)=15<BR>\n" );
document.write( "multiply by 2x<BR>\n" );
document.write( "6x^2+36=30x<BR>\n" );
document.write( "6x^2-30x+36=0<BR>\n" );
document.write( "/6<BR>\n" );
document.write( "x^2-5x+6=0<BR>\n" );
document.write( "x^2-3x-2x+6=0<BR>\n" );
document.write( "x(x-3)-2(x-3)=0<BR>\n" );
document.write( "(x-3)(x-2)=0<BR>\n" );
document.write( "x=3 OR x=2<BR>\n" );
document.write( "...<BR>\n" );
document.write( "plug value of x in the equation 2xy=9<BR>\n" );
document.write( "2*3*y=9<BR>\n" );
document.write( "6y=9<BR>\n" );
document.write( "y=9/6<BR>\n" );
document.write( "y=3/2<BR>\n" );
document.write( "(3,3/2)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "2*2*y=9<BR>\n" );
document.write( "4y=9<BR>\n" );
document.write( "y=9/4<BR>\n" );
document.write( "(2,9/4)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Distance = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distance =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%283-2%29%5E2%2B%28%283%2F2%29-%289%2F4%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%283-2%29%5E2%2B%28%283%2F2%29-%289%2F4%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distance= 1.25<BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%28%28-3x%2F4%29%2B%2815%2F4%29%29%2C%289%2F2x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%28%28-3x%2F4%29%2B%2815%2F4%29%29%2C%289%2F2x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );