document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40824>Question 40824</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve this system of equation:<BR>\n" );
document.write( "x^2+y^2=36<BR>\n" );
document.write( "x+y=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26228 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, graphing might help but is often not precise enough to give a perfect solution...your best bet is to do it using algebra by solving the second equation for x or y and then plugging it in to the first...like this...<BR>\n" );
document.write( "x^2+y^2=36<BR>\n" );
document.write( "x+y=4<BR>\n" );
document.write( "gives<BR>\n" );
document.write( "y = 4 - x and<BR>\n" );
document.write( "x^2 + (4 - x)^2 = 36<BR>\n" );
document.write( "x^2 + 16 - 8x + x^2 = 36<BR>\n" );
document.write( "2x^2 - 8x - 20 = 0<BR>\n" );
document.write( "x^2 - 4x - 10 = 0 (can't factor, use quadratic)<BR>\n" );
document.write( "x = (4 ± sqrt(16 + 40)) / 2<BR>\n" );
document.write( "x = (4 ± 2*sqrt(14)) / 2<BR>\n" );
document.write( "x = 2 ± sqrt(14)<BR>\n" );
document.write( "Now plug either of these solutions into the second eqn to get the y's that correspond to each x...<BR>\n" );
document.write( "y = 4 - (2 + sqrt(14) = 2 - sqrt(14)<BR>\n" );
document.write( "y = 4 - (2 - sqrt(14) = 2 + sqrt(14) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );