document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62040>Question 62040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I tried to follow the directions on the video, but I got lost somewhere and messed up.  I am lost.\r<BR>\n" );
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document.write( "Solve each of the following systems.<BR>\n" );
document.write( "(1) x + y = 5<BR>\n" );
document.write( "    x^2 + y = 5\r<BR>\n" );
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document.write( "(2) x - y = 2<BR>\n" );
document.write( "    x^2 + y^2 = 4\r<BR>\n" );
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document.write( "(3) x^2 + y^2 = 12<BR>\n" );
document.write( "    x^2 + y = 10\r<BR>\n" );
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document.write( "(4) x^3 - 2^x - 5X + 6 = 0<BR>\n" );
document.write( "    3x - y + 6 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42802 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=42802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1)<BR>\n" );
document.write( "x + y = 5 is also ~> y = 5 - x<BR>\n" );
document.write( "x^2 + y = 5<BR>\n" );
document.write( "x^2 + 5 - x = 5 Remember you can substitute the 5 - x in for y<BR>\n" );
document.write( "x^2 - x = 0<BR>\n" );
document.write( "x(x - 1) = 0<BR>\n" );
document.write( "x = 0 and x = 1<BR>\n" );
document.write( "Plug:<BR>\n" );
document.write( "y = 5 - x<BR>\n" );
document.write( "(0,5) and (1,4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C5+-+x%2C5+-+x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C5+-+x%2C5+-+x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "x - y = 2 is also ~> x = 2 + y<BR>\n" );
document.write( "x^2 + y^2 = 4<BR>\n" );
document.write( "(2 + y)^2 + y^2 = 4<BR>\n" );
document.write( "4 + 4y + y^2 + y^2 = 4<BR>\n" );
document.write( "2y^2 + 4y = 0<BR>\n" );
document.write( "y^2 + 2y = 0<BR>\n" );
document.write( "y(y + 2) = 0<BR>\n" );
document.write( "y = 0 and y = -2<BR>\n" );
document.write( "Plug:<BR>\n" );
document.write( "x = 2 + y<BR>\n" );
document.write( "(2,0) and (0,-2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx+-+2%2C+sqrt%284+-+x%5E2%29%2C+-sqrt%284+-+x%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3)<BR>\n" );
document.write( "x^2 + y^2 = 12 is also ~> x^2 = 12 - y^2<BR>\n" );
document.write( "x^2 + y = 10<BR>\n" );
document.write( "12 - y^2 + y = 10<BR>\n" );
document.write( "-y^2 + y + 2 = 0<BR>\n" );
document.write( "(y + 1)(-y + 2) = 0<BR>\n" );
document.write( "y = -1 and y = 2<BR>\n" );
document.write( "Plug:<BR>\n" );
document.write( "x^2 = 12 - y^2<BR>\n" );
document.write( "x = +- sqrt(12 - y^2)<BR>\n" );
document.write( "x = +- sqrt(12 - 1) = +- sqrt(11)<BR>\n" );
document.write( "(sqrt(11),-1)<BR>\n" );
document.write( "(-sqrt(11),-1)<BR>\n" );
document.write( "x = +- sqrt(12 - y^2) = +- sqrt(12 - 4) = +- sqrt(8)<BR>\n" );
document.write( "(sqrt(8),2)<BR>\n" );
document.write( "(-sqrt(8),2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Csqrt%2812+-+x%5E2%29%2C-sqrt%2812+-+x%5E2%29%2C10+-+x%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4)<BR>\n" );
document.write( "3x - y + 6 = 0 ~> red line demonstrates this line<BR>\n" );
document.write( "x^3 - x^2 - 5x + 6 = 0 ~> found from green line (x-intercepts are answers)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x+%2B+6%2Cx%5E3+-+x%5E2+-+5x+%2B+6%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x+%2B+6%2Cx%5E3+-+x%5E2+-+5x+%2B+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );