document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=441886>Question 441886</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of equations and state answer in coordinate pairs?x^(2)+y^(2)=15 and x^(2)+y=-15\r<BR>\n" );
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document.write( "answers...(21,6)(10,-5),(21,-6)(-10,-5),(21,6)(-10,-5), no solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #304879 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=304879\">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=x%5E2+%2B+y%5E2+=+15 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y+=+-15 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]<BR>\n" );
document.write( "Subtract equation 2 from equation 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+y+=+30+-%3E+y%5E2+-+y+-+30+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+-+y+=+30+-%3E+y%5E2+-+y+-+30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula to solve for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281+%2B-+sqrt%281%2B120%29%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%281+%2B-+sqrt%281%2B120%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281+%2B-+11%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%281+%2B-+11%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = -5,6<BR>\n" );
document.write( "If we use equation [2] to find x, we see that no solution exists for either value of y:<BR>\n" );
document.write( "y=-5: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5+=+-15+-%3E+x%5E2+%3C+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+5+=+-15+-%3E+x%5E2+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y=6:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6+=+-15+-%3E+x%5E2+%3C+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6+=+-15+-%3E+x%5E2+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So there is no solution.  <BR>\n" );
document.write( "This can also be seen by the graphs of the two functions.  Notice there are no points of intersection:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-30%2C30%2C-30%2C30%2Csqrt%2815-x%5E2%29%2C-sqrt%2815-x%5E2%29%2C-15-x%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );