document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473678>Question 473678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 1/x+1/y=1/4 and 1/x-1/y=3/4,then x=<BR>\n" );
document.write( "(A)1/4<BR>\n" );
document.write( "(B)1/2<BR>\n" );
document.write( "(C)1<BR>\n" );
document.write( "(D)2<BR>\n" );
document.write( "(E)4\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324958 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equations you have to work with are:<BR>\n" );
document.write( "1/x + 1/y = 1/4 (first equation)<BR>\n" );
document.write( "1/x - 1/y = 3/4 (second equation)<BR>\n" );
document.write( "solve these 2 equations simultaneously to get your answer.<BR>\n" );
document.write( "use the first equation to solve for 1/x.<BR>\n" );
document.write( "1/x + 1/y = 1/4 becomes 1/x = 1/4 - 1/y<BR>\n" );
document.write( "we can substitute for 1/x in the second equation to get:<BR>\n" );
document.write( "1/x - 1/y = 3/4 becomes:<BR>\n" );
document.write( "(1/4 - 1/y) - 1/y = 3/4<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "1/4 - 1/y - 1/y = 3/4<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "1/4 - 2/y = 3/4<BR>\n" );
document.write( "subtract 1/4 from both sides of this equation to get:<BR>\n" );
document.write( "-2/y = 1/2<BR>\n" );
document.write( "divide both sides of this equation by -2 to ge4t:<BR>\n" );
document.write( "1/y = -1/4<BR>\n" );
document.write( "now that we know what 1/y is equal to, we can solve for 1/x.<BR>\n" );
document.write( "use the first equation of:<BR>\n" );
document.write( "1/x + 1/y = 1/4<BR>\n" );
document.write( "substitute -1/4 for 1/y to get:<BR>\n" );
document.write( "1/x - 1/4 = 1/4<BR>\n" );
document.write( "add 1/4 to both sides of this equation to get:<BR>\n" );
document.write( "1/x = 1/2<BR>\n" );
document.write( "you now have:<BR>\n" );
document.write( "1/x = 1/2<BR>\n" );
document.write( "1/y = -1/4<BR>\n" );
document.write( "solve for x in the first of these 2 equations.<BR>\n" );
document.write( "1/x = 1/2 is the equation.<BR>\n" );
document.write( "multiply both sides of this equation by x to get:<BR>\n" );
document.write( "|1 = x/2<BR>\n" );
document.write( "multiply both sides of this equation by 2 to get:<BR>\n" );
document.write( "2 = x which is the same as x = 2.<BR>\n" );
document.write( "that's your answer.<BR>\n" );
document.write( "selection D contains it.<BR>\n" );
document.write( "similarly, we can solve for y to get y = -4<BR>\n" );
document.write( "we have x = 2 and y = -4<BR>\n" );
document.write( "substitute in your original equations to see that these solutions are good for both equations.<BR>\n" );
document.write( "1/x + 1/y = 1/4 becomes 1/2 - 1/4 = 1/4 which is true.<BR>\n" );
document.write( "1/x - 1/y = 3/4 becomes 1/2 + 1/4 = 3/4 which is also true.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );