document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957021>Question 957021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following systems of two circles by finding the intersection point(s), if any, algebraically.\r<BR>\n" );
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document.write( "x^2 + y^2 = 9<BR>\n" );
document.write( "(x-3)^2 + (y+3)^2 =9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584886 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=584886\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+=9-+%28y%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+=9-+%28y%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0+%2B-+sqrt%289-+%28y%2B3%29%5E2%29 ALIGN=MIDDLE  ALT=\"x-3=0+%2B-+sqrt%289-+%28y%2B3%29%5E2%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=3+%2B-+sqrt%289-+%28y%2B3%29%5E2%29 ALIGN=MIDDLE  ALT=\"x=3+%2B-+sqrt%289-+%28y%2B3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=9%2B6sqrt%289-%28y%2B3%29%5E2%29%2B9-%28y%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2=9%2B6sqrt%289-%28y%2B3%29%5E2%29%2B9-%28y%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-Positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=9-6sqrt%289-%28y%2B3%29%5E2%29%2B9-%28y%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2=9-6sqrt%289-%28y%2B3%29%5E2%29%2B9-%28y%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-Negative<BR>\n" );
document.write( "Substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2B6sqrt%289-%28y%2B3%29%5E2%29%2B9-%28y%2B3%29%5E2%29+%2B+y%5E2+=+9 ALIGN=MIDDLE  ALT=\"%289%2B6sqrt%289-%28y%2B3%29%5E2%29%2B9-%28y%2B3%29%5E2%29+%2B+y%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >-Positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-6sqrt%289-%28y%2B3%29%5E2%29%2B9-%28y%2B3%29%5E2%29+%2B+y%5E2+=+9 ALIGN=MIDDLE  ALT=\"%289-6sqrt%289-%28y%2B3%29%5E2%29%2B9-%28y%2B3%29%5E2%29+%2B+y%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >-Negative<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6sqrt%289-%28y%2B3%29%5E2%29%2B9-y%5E2-6y-9+%2B+y%5E2+=+0 ALIGN=MIDDLE  ALT=\"6sqrt%289-%28y%2B3%29%5E2%29%2B9-y%5E2-6y-9+%2B+y%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-Positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6sqrt%289-%28y%2B3%29%5E2%29%2B9-y%5E2-6y-9+%2B+y%5E2+=+0 ALIGN=MIDDLE  ALT=\"-6sqrt%289-%28y%2B3%29%5E2%29%2B9-y%5E2-6y-9+%2B+y%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-Negative<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289-%28y%2B3%29%5E2%29=y++ ALIGN=MIDDLE  ALT=\"sqrt%289-%28y%2B3%29%5E2%29=y++\"   DISABLED_style= \"max-width:90%; height:auto;\" >-Positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%289-%28y%2B3%29%5E2%29=y++ ALIGN=MIDDLE  ALT=\"-sqrt%289-%28y%2B3%29%5E2%29=y++\"   DISABLED_style= \"max-width:90%; height:auto;\" >-Negative<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-%28y%2B3%29%5E2=y%5E2 ALIGN=MIDDLE  ALT=\"9-%28y%2B3%29%5E2=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-y%5E2-6y-9=y%5E2 ALIGN=MIDDLE  ALT=\"9-y%5E2-6y-9=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2%2B6y=0 ALIGN=MIDDLE  ALT=\"2y%5E2%2B6y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28y%2B3%29=0 ALIGN=MIDDLE  ALT=\"y%28y%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+%2B+%280%2B3%29%5E2+=9 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+%2B+%280%2B3%29%5E2+=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   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%2B3=0 ALIGN=MIDDLE  ALT=\"y%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3 ALIGN=MIDDLE  ALT=\"y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28-3%29%5E2=9 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28-3%29%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3,0) and (0,-3)<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C6%2C-6%2C4%2Cgrid%281%29%2Ccircle%280%2C0%2C3%29%2Ccircle%283%2C-3%2C3%29%2Ccircle%283%2C0%2C0.2%29%2Ccircle%280%2C-3%2C0.2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );