document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066108>Question 1066108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simaltaneous linear and quadratic equation <BR>\n" );
document.write( " <BR>\n" );
document.write( "Y=2x+5,Y=2x^2-x+3  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681272 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=681272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+%2B+5+ ALIGN=MIDDLE  ALT=\"+y+=+2x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x%5E2+-+x+%2B+3+ ALIGN=MIDDLE  ALT=\"+y+=+2x%5E2+-+x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+5+=+2%2Ax%5E2+-+x+%2B+3+ ALIGN=MIDDLE  ALT=\"+2x+%2B+5+=+2%2Ax%5E2+-+x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E2+-+3x+-+2+=+0+ ALIGN=MIDDLE  ALT=\"+2x%5E2+-+3x+-+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2+ ALIGN=MIDDLE  ALT=\"+a+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-3+ ALIGN=MIDDLE  ALT=\"+b+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-2+ ALIGN=MIDDLE  ALT=\"+c+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A%28-2%29+%29%29+%2F+%282%2A2%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A%28-2%29+%29%29+%2F+%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+3+%2B-+sqrt%28+9+%2B+16+%29%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%28+3+%2B-+sqrt%28+9+%2B+16+%29%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+3+%2B-+sqrt%28+25+%29+%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%28+3+%2B-+sqrt%28+25+%29+%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+3+%2B+5+%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%28+3+%2B+5+%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2+ ALIGN=MIDDLE  ALT=\"+x+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+3+-+5+%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%28+3+-+5+%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-2%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+-2%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-1%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Plug the x's back into (1) or (2) to get y's<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+%2B+5+ ALIGN=MIDDLE  ALT=\"+y+=+2x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2%2A2+%2B+5+ ALIGN=MIDDLE  ALT=\"+y+=+2%2A2+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+9+ ALIGN=MIDDLE  ALT=\"+y+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+%2B+5+ ALIGN=MIDDLE  ALT=\"+y+=+2x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2%2A%28-1%2F2%29+%2B+5+ ALIGN=MIDDLE  ALT=\"+y+=+2%2A%28-1%2F2%29+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-1+%2B+5+ ALIGN=MIDDLE  ALT=\"+y+=+-1+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4+ ALIGN=MIDDLE  ALT=\"+y+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "The intersections are:<BR>\n" );
document.write( "( 2, 9 ) and ( -1/2, 4 )<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x%5E2+-+x+%2B+3+ ALIGN=MIDDLE  ALT=\"+y+=+2x%5E2+-+x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2%2A2%5E2+-+2+%2B+3+ ALIGN=MIDDLE  ALT=\"+y+=+2%2A2%5E2+-+2+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+8+-+2+%2B+3+ ALIGN=MIDDLE  ALT=\"+y+=+8+-+2+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+9+ ALIGN=MIDDLE  ALT=\"+y+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "You can check ( -1/2, 4 )<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+10%2C+2x+%2B+5%2C+2x%5E2+-+x+%2B+3+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+10%2C+2x+%2B+5%2C+2x%5E2+-+x+%2B+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );