document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765924>Question 765924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1...The sum of the two squares of two numbers is 4 and the difference of the squares of those two numbers is 1. Find the numbers\r<BR>\n" );
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document.write( "2...The sum of the square of the first number and the twice of the square of the second number is 6 and the twice of the first number take away the second number is 2. Find the two numbers.\r<BR>\n" );
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document.write( "Thanks :D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466510 by </B><A HREF=/tutors/aboutme.mpl?userid=MaartenRU><B>MaartenRU(13)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MaartenRU><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=MaartenRU><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=466510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.\r<BR>\n" );
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document.write( "Let's call the two numbers x and y. Then <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=4 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can see that, by subtracting the second equation from the first one, that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2=3 ALIGN=MIDDLE  ALT=\"2y%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=3%2F2 ALIGN=MIDDLE  ALT=\"y%5E2=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%283%2F2%29 ALIGN=MIDDLE  ALT=\"y=sqrt%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-sqrt%283%2F2%29 ALIGN=MIDDLE  ALT=\"y=-sqrt%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting this into the first equation gives us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3%2F2=4 ALIGN=MIDDLE  ALT=\"x%5E2%2B3%2F2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=5%2F2 ALIGN=MIDDLE  ALT=\"x%5E2=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%285%2F2%29 ALIGN=MIDDLE  ALT=\"x=sqrt%285%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%285%2F2%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%285%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "Same idea here. We're calling the two numbers x and y. We get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2y%5E2=6 ALIGN=MIDDLE  ALT=\"x%5E2%2B2y%5E2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=2 ALIGN=MIDDLE  ALT=\"2x-y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the problem is a bit trickier though. We can't really find the value of either x or y immediately, so we're going to use substitution.\r<BR>\n" );
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document.write( "According to the second equation, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y=2 ALIGN=MIDDLE  ALT=\"2x-y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can rewrite this as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-2 ALIGN=MIDDLE  ALT=\"y=2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we substitute this 'implicit' value of y into our first equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2%282x-2%29%5E2=6 ALIGN=MIDDLE  ALT=\"x%5E2%2B2%282x-2%29%5E2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We'll make that a bit nicer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2%282x-2%29%5E2=x%5E2%2B2%284x%5E2-8x%2B4%29=x%5E2%2B8x%5E2-16x%2B8=9x%5E2-16x%2B8=6 ALIGN=MIDDLE  ALT=\"x%5E2%2B2%282x-2%29%5E2=x%5E2%2B2%284x%5E2-8x%2B4%29=x%5E2%2B8x%5E2-16x%2B8=9x%5E2-16x%2B8=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-16x%2B2=0 ALIGN=MIDDLE  ALT=\"9x%5E2-16x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, that's an equation we can solve. With the trusty old<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We get <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2816%2B-sqrt%28256-4%2A9%2A2%29%29%2F%282%2A9%29=%2816%2B-sqrt%28256-72%29%29%2F18=%2816%2B-sqrt%28184%29%29%2F18 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing the numerator and denominator by two gives us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F9%29%2A%288%2B-sqrt%2846%29%29 ALIGN=MIDDLE  ALT=\"x=%281%2F9%29%2A%288%2B-sqrt%2846%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-2=2%2A%281%2F9%29%2A%288%2B-sqrt%2846%29%29-2 ALIGN=MIDDLE  ALT=\"y=2x-2=2%2A%281%2F9%29%2A%288%2B-sqrt%2846%29%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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