document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166393>Question 166393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the system of equations y=x^4-3x³ and y=2x-6. Find the points of intersection. Give an exact answer. PLEASE HELP ME! I don't know what to do!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122633 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122633\">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=+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+2x-6%2C+x%5E4-3x%5E3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+2x-6%2C+x%5E4-3x%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A closer look<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-1%2C+5%2C+-5%2C+5%2C+2x-6%2C+x%5E4-3x%5E3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-1%2C+5%2C+-5%2C+5%2C+2x-6%2C+x%5E4-3x%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looks like (3,0) may be an intersection point.<BR>\n" );
document.write( "Try it.<BR>\n" );
document.write( "y=2x-6<BR>\n" );
document.write( "0=2(3)-6<BR>\n" );
document.write( "0=0<BR>\n" );
document.write( "True.<BR>\n" );
document.write( "y=x^4-3x^3<BR>\n" );
document.write( "0=3^4-3(3^3)<BR>\n" );
document.write( "0=0<BR>\n" );
document.write( "True<BR>\n" );
document.write( "(3,0) is a solution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-1%2C+3%2C+-5%2C+1%2C+2x-6%2C+x%5E4-3x%5E3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-1%2C+3%2C+-5%2C+1%2C+2x-6%2C+x%5E4-3x%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Can't find the second solution exactly by graphing. <BR>\n" );
document.write( "Iteration is required. <BR>\n" );
document.write( "x=1.25 is a good start point.<BR>\n" );
document.write( "Iteration leads to x=1.259922 with corresponding y=-3.48016.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-1%2C+3%2C+-5%2C+1%2Cgrid%28+1+%29%2Ccircle%28+1.259922%2C+-3.48016%2C+.1+%29%2Cgraph%28+300%2C+300%2C+-1%2C+3%2C+-5%2C+1%2C+2x-6%2C+x%5E4-3x%5E3%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );