document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209168>Question 1209168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all ordered pairs (x,y) of real numbers such that x + y = 10 and x^2 + y^2 = 62 + 2xy.\r<BR>\n" );
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document.write( "For example, to enter the solutions (2,4) and (-3,9), you would enter \"(2,4),(-3,9)\"  (without the quotation marks). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847749 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=10 ALIGN=MIDDLE  ALT=\"x%2By=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=62%2B2xy ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=62%2B2xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Whenever the given equations have terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy ALIGN=MIDDLE  ALT=\"2xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >, one thing you want to look at is using one of these:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E2=x%5E2%2B2xy%2By%5E2 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E2=x%5E2%2B2xy%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%5E2=x%5E2-2xy%2By%5E2 ALIGN=MIDDLE  ALT=\"%28x-y%29%5E2=x%5E2-2xy%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For this problem....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=62%2B2xy ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=62%2B2xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2xy%2By%5E2=62 ALIGN=MIDDLE  ALT=\"x%5E2-2xy%2By%5E2=62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%5E2=62 ALIGN=MIDDLE  ALT=\"%28x-y%29%5E2=62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve the first given equation for y in terms of x and substitute in this last equation.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10-x ALIGN=MIDDLE  ALT=\"y=10-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=x-%2810-x%29=x-10%2Bx=2x-10 ALIGN=MIDDLE  ALT=\"x-y=x-%2810-x%29=x-10%2Bx=2x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%5E2=%282x-10%29%5E2=62 ALIGN=MIDDLE  ALT=\"%28x-y%29%5E2=%282x-10%29%5E2=62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-40x%2B100=62 ALIGN=MIDDLE  ALT=\"4x%5E2-40x%2B100=62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-40x%2B38=0 ALIGN=MIDDLE  ALT=\"4x%5E2-40x%2B38=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That quadratic does not factor, so use the quadratic formula to find<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2840%2Bsqrt%28992%29%29%2F8 ALIGN=MIDDLE  ALT=\"x=%2840%2Bsqrt%28992%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2840-sqrt%28992%29%29%2F8 ALIGN=MIDDLE  ALT=\"x=%2840-sqrt%28992%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Partially simplified, those roots are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Bsqrt%28992%29%2F8 ALIGN=MIDDLE  ALT=\"5%2Bsqrt%28992%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-sqrt%28992%29%2F8 ALIGN=MIDDLE  ALT=\"5-sqrt%28992%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The given equations are symmetrical in x and y, so the two solutions are that x and y are equal to, in either order, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Bsqrt%28992%29%2F8 ALIGN=MIDDLE  ALT=\"5%2Bsqrt%28992%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-sqrt%28992%29%2F8 ALIGN=MIDDLE  ALT=\"5-sqrt%28992%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Those numbers, confirmed by graphing the system of equations using desmos.com, are approximately 8.937 and 1.063.<br><BR>\n" );
document.write( "ANSWERS (approximately): (8.937,1.603) and (1.063,8.937)<br><BR>\n" );
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