document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30458>Question 30458</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (8) Question:<BR>\n" );
document.write( "How many solutions does this nonlinear system have?<BR>\n" );
document.write( "2y=2x^2+4x+9<BR>\n" );
document.write( "y=x^2+2x+3\r<BR>\n" );
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document.write( "(A) 0<BR>\n" );
document.write( "(B) 1<BR>\n" );
document.write( "(C) 2<BR>\n" );
document.write( "(D) 3<BR>\n" );
document.write( "(E) Infinite solutions\r<BR>\n" );
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document.write( "Thanks!<BR>\n" );
document.write( "PLEASE NOTE THIS IS THE CORRECT QUESTION AND WRITTEN EXACTLY HOW IT IS FOUND IN MY WORK ~ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17231 by </B><A HREF=/tutors/aboutme.mpl?userid=Fermat><B>Fermat(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fermat><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=Fermat><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are no solutions!<BR>\n" );
document.write( "Your two eqns are,<BR>\n" );
document.write( "2y=2x^2+4x+9<BR>\n" );
document.write( "y=x^2+2x+3<BR>\n" );
document.write( "Dividing the top eqn by 2, the system of eqns becomes,<BR>\n" );
document.write( "y=x^2+2x+4.5<BR>\n" );
document.write( "y=x^2+2x+3<BR>\n" );
document.write( "These are two \"parallel\" curves (parabolas).<BR>\n" );
document.write( "One parabola cuts the y-axis at y = 4.5.<BR>\n" );
document.write( "The other parabola cuts the y-axis at y = 3.<BR>\n" );
document.write( "The two parabolas are the same size/shape and will never intersect, hence no solutions.<BR>\n" );
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