document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=348952>Question 348952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations:\r<BR>\n" );
document.write( "\n" );
document.write( "x + y + square root(xy) = 28<BR>\n" );
document.write( "x^2 + y^2 + xy = 336 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #249741 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=249741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations:<BR>\n" );
document.write( "x + y + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28xy%29 ALIGN=MIDDLE  ALT=\"sqrt%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 28<BR>\n" );
document.write( "x^2 + y^2 + xy = 336<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Simplify the 1st equation to use for elimination<BR>\n" );
document.write( "x + y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28+-+sqrt%28xy%29 ALIGN=MIDDLE  ALT=\"28+-+sqrt%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2xy+%2B+y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2xy+%2B+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=784+-+56sqrt%28xy%29+%2B+xy ALIGN=MIDDLE  ALT=\"784+-+56sqrt%28xy%29+%2B+xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract xy from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2xy+-+xy%2B+y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2xy+-+xy%2B+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=784+-+56sqrt%28xy%29 ALIGN=MIDDLE  ALT=\"784+-+56sqrt%28xy%29\"   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+%2B+xy%2B+y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+xy%2B+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=784+-+56sqrt%28xy%29 ALIGN=MIDDLE  ALT=\"784+-+56sqrt%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use for elimination with 2nd equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2%2B+xy ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2%2B+xy\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=784+-+56sqrt%28xy%29 ALIGN=MIDDLE  ALT=\"784+-+56sqrt%28xy%29\"   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+%2B+y%5E2+%2B+xy+=+336 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+%2B+xy+=+336\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------Subtraction eliminates everything on the left, we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+448+-+56sqrt%28xy%29 ALIGN=MIDDLE  ALT=\"0+=+448+-+56sqrt%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56sqrt%28xy%29+=+448 ALIGN=MIDDLE  ALT=\"56sqrt%28xy%29+=+448\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by 56, results:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28xy%29+=+8 ALIGN=MIDDLE  ALT=\"sqrt%28xy%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "xy = 64<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Fx ALIGN=MIDDLE  ALT=\"64%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Fx ALIGN=MIDDLE  ALT=\"64%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > for y in the 1st equation<BR>\n" );
document.write( "x + y + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28xy%29 ALIGN=MIDDLE  ALT=\"sqrt%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 28<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Fx ALIGN=MIDDLE  ALT=\"64%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2864%2Fx%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2864%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 28<BR>\n" );
document.write( "x's inside the radical cancel<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Fx ALIGN=MIDDLE  ALT=\"64%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2864%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 28<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Fx ALIGN=MIDDLE  ALT=\"64%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 8 = 28<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Fx ALIGN=MIDDLE  ALT=\"64%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 28 - 8<BR>\n" );
document.write( "x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Fx ALIGN=MIDDLE  ALT=\"64%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20<BR>\n" );
document.write( "multiply by x<BR>\n" );
document.write( "x^2 + 64 = 20x<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "x^2 - 20x + 64 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x-16)(x-4)<BR>\n" );
document.write( "x = 16<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find y:<BR>\n" );
document.write( "When x=16: y = 64/16 = 4<BR>\n" );
document.write( "When x=4: y = 64/4 = 16<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution in the 1st equation<BR>\n" );
document.write( "16 + 4 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2A4%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 28<BR>\n" );
document.write( "20 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864%29 ALIGN=MIDDLE  ALT=\"sqrt%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 28; confirms our solutions; x=16, y-4 and x=4, y=16 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );