document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=658079>Question 658079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the sum of two numbers is 19 and the sum of their squares is 221. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410146 by </B><A HREF=/tutors/aboutme.mpl?userid=aaronwiz><B>aaronwiz(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aaronwiz><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=410146\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, my name is Aaron I am in 10th grade and im in honors trig/pre-calc. <BR>\n" );
document.write( "let<BR>\n" );
document.write( "x=first number<BR>\n" );
document.write( "y=second number\r<BR>\n" );
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document.write( "x+y=19<BR>\n" );
document.write( "x^2+Y^2=221\r<BR>\n" );
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document.write( "x=19-y<BR>\n" );
document.write( "x^2+Y^2=221\r<BR>\n" );
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document.write( "Now simply substitute\r<BR>\n" );
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document.write( "(19-y)^2+y^2=221\r<BR>\n" );
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document.write( "foil\r<BR>\n" );
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document.write( "(361-38y+y^2)+y^2=221\r<BR>\n" );
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document.write( "put into standard form\r<BR>\n" );
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document.write( "2y^2-38y+140=0\r<BR>\n" );
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document.write( "simplify\r<BR>\n" );
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document.write( "y^2-19y+70=0\r<BR>\n" );
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document.write( "factor\r<BR>\n" );
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document.write( "(y-14)(y-5)=0\r<BR>\n" );
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document.write( "y=14 or 5\r<BR>\n" );
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document.write( "plug y=5 back in to x^2+Y^2=221\r<BR>\n" );
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document.write( "25+x^2=221<BR>\n" );
document.write( "x^2=196 <BR>\n" );
document.write( "thus x= plus or minus 14 when y=5\r<BR>\n" );
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document.write( "plug y=14 back in to x^2+Y^2=221<BR>\n" );
document.write( "x^2+196=221<BR>\n" );
document.write( "x^2=25<BR>\n" );
document.write( "thus x= plus or minus 5 when y=14\r<BR>\n" );
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document.write( "However when negative numbers are plugged into x+y=19 it is never true. That means only positive solutions work. So one of the numbers is 5 and the other one is 14.\r<BR>\n" );
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document.write( "Hope I helped. I would really appreciate your recommendation, their are plenty of other things I could be doing rather then spending time on this site helping people. Good luck! :)  </SPAN>\n" );
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