document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=216636>Question 216636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the coordinates of the points of intersection for the graphs of <BR>\n" );
document.write( "x^2 + 2y^2 = 33 and x^2 + y^2 = 2x + 19\r<BR>\n" );
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document.write( "a)(5,2),(-1,4)<BR>\n" );
document.write( "b)(5,4),(-1,2)<BR>\n" );
document.write( "c)(5,+-2),(-1,+-4)<BR>\n" );
document.write( "d)graphs do not intersect </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163568 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=163568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll give you a hint to get started\r<BR>\n" );
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document.write( "First, note that there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms.\r<BR>\n" );
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document.write( "So take the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=2x%2B19 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=2x%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I'm going to choose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=-x%5E2%2B2x%2B19 ALIGN=MIDDLE  ALT=\"y%5E2=-x%5E2%2B2x%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now simply plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=-x%5E2%2B2x%2B19 ALIGN=MIDDLE  ALT=\"y%5E2=-x%5E2%2B2x%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2y%5E2=33 ALIGN=MIDDLE  ALT=\"x%5E2%2B2y%5E2=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2%28-x%5E2%2B2x%2B19%29=33 ALIGN=MIDDLE  ALT=\"x%5E2%2B2%28-x%5E2%2B2x%2B19%29=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now just solve the equation above to find 'x' and then use the value(s) of 'x' to find the corresponding value(s) of 'y'. </SPAN>\n" );
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