document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199494>Question 1199494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following non-linear systems and graph in the cartesian plane. You can use either Elimination, Substitution and make sure to identify the solutions by Graphing Method. Show your Complete Solution.\r<BR>\n" );
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document.write( "3x+2y=8<BR>\n" );
document.write( "x^2+y^2=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833413 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x+2y=8<BR>\n" );
document.write( "x^2+y^2=8<BR>\n" );
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document.write( "3x+2y=8 ---> y = -(3/2)x + 4<BR>\n" );
document.write( "y^2 = (9x^2/4) - 12x + 16<BR>\n" );
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document.write( "x^2+y^2=8<BR>\n" );
document.write( "Sub for y^2<BR>\n" );
document.write( "x^2 + (9x^2/4) - 12x + 16 = 8<BR>\n" );
document.write( "4x^2 + 9x^2 - 48x + 32 = 0<BR>\n" );
document.write( "13x^2 - 48x + 32 = 0<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%5E2%2B-48x%2B32+=+0 ALIGN=MIDDLE  ALT=\"13x%5E2%2B-48x%2B32+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-48%29%5E2-4%2A13%2A32=640 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-48%29%5E2-4%2A13%2A32=640\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=640 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--48%2B-sqrt%28+640+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--48%2B-sqrt%28+640+%29%29%2F2%5Ca\"   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%5B1%5D+=+%28-%28-48%29%2Bsqrt%28+640+%29%29%2F2%5C13+=+2.81916235697489 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-48%29%2Bsqrt%28+640+%29%29%2F2%5C13+=+2.81916235697489\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-48%29-sqrt%28+640+%29%29%2F2%5C13+=+0.873145335332806 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-48%29-sqrt%28+640+%29%29%2F2%5C13+=+0.873145335332806\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%5E2%2B-48x%2B32 ALIGN=MIDDLE  ALT=\"13x%5E2%2B-48x%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%5E2%2B-48x%2B32+=+%28x-2.81916235697489%29%2A%28x-0.873145335332806%29 ALIGN=MIDDLE  ALT=\"13x%5E2%2B-48x%2B32+=+%28x-2.81916235697489%29%2A%28x-0.873145335332806%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.81916235697489, 0.873145335332806.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+13%2Ax%5E2%2B-48%2Ax%2B32+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+13%2Ax%5E2%2B-48%2Ax%2B32+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Sub for x in 3x+2y=8 and find y.<BR>\n" );
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document.write( "For the graph, DL the FREE software at www.padowan.dk<BR>\n" );
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document.write( "Use F6 to enter the given relationships.\r<BR>\n" );
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