document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170266>Question 170266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help On This Will Be Great Appreciated<3<BR>\n" );
document.write( "Solve The Non-Linear system of Equations. Give Exact Values.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=10 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=x%5E2%2B8 ALIGN=MIDDLE  ALT=\"3y=x%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125692 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=125692\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2+=+10 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+x%5E2%2B8 ALIGN=MIDDLE  ALT=\"3y+=+x%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite this as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+3y-8 ALIGN=MIDDLE  ALT=\"x%5E2+=+3y-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute into the 1st equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283y-8%29%2By%5E2+=+10 ALIGN=MIDDLE  ALT=\"%283y-8%29%2By%5E2+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B3y-18+=+0 ALIGN=MIDDLE  ALT=\"y%5E2%2B3y-18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-3%29%28y%2B6%29+=+0 ALIGN=MIDDLE  ALT=\"%28y-3%29%28y%2B6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product rule.<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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6 ALIGN=MIDDLE  ALT=\"y+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the positive solution and substitute into the second equation to solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+x%5E2%2B8 ALIGN=MIDDLE  ALT=\"3y+=+x%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute y = 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%283%29+=+x%5E2%2B8 ALIGN=MIDDLE  ALT=\"3%283%29+=+x%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 8 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-8+=+x%5E2 ALIGN=MIDDLE  ALT=\"9-8+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution consists of two points of intersection:<BR>\n" );
document.write( "(1, 3) and (-1, 3)<BR>\n" );
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document.write( "Just for interest, since we had two solutions for y (y = 3 and y = -6), let's see what happens when we choose the second solution of y = -6 and substitute into the first equation to solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+x%5E2%2B8 ALIGN=MIDDLE  ALT=\"3y+=+x%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute y = -6.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-6%29+=+x%5E2%2B8 ALIGN=MIDDLE  ALT=\"3%28-6%29+=+x%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 8 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+-26 ALIGN=MIDDLE  ALT=\"x%5E2+=+-26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%28-26%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-26%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%28-26%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-26%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and, as you can see, the results are \"imaginary\" numbers, so there is no \"real\" solution for y = -6.<BR>\n" );
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document.write( "Let's see what the graph of these two functions look like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Csqrt%28-x%5E2%2B10%29%2C-sqrt%28-x%5E2%2B10%29%2C%281%2F3%29x%5E2%2B8%2F3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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