document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884679>Question 884679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solving quadratic systems. Also asked to state which conic section each equation represents. (Circle, parabolas, etc). Please explain how to solve 4x^2+9y^2=144<BR>\n" );
document.write( "                                                                                             2x+3y=12 either by elimination or substitution. Also advise how would I know which conic section to chose. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534555 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=534555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ellipse,   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B9y%5E2=144 ALIGN=MIDDLE  ALT=\"4x%5E2%2B9y%5E2=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".                                                                                 Line,   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y=12 ALIGN=MIDDLE  ALT=\"2x%2B3y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can identify the type of conic section just by looking at those equations.  The ellipse equation is almost but not yet in standard form and the line is in standard form.  Identification is uncomplicated.\r<BR>\n" );
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document.write( "Solving the system of the two equations is a little more work.<BR>\n" );
document.write( "Solve the linear equation for either variable and substitute into the ellipse equation and solve for the single variable.  You could use the linear equation again to determine the other variable.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=-2x%2B12 ALIGN=MIDDLE  ALT=\"3y=-2x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2F3%2B4 ALIGN=MIDDLE  ALT=\"y=-2x%2F3%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B9%28-2x%2F3%2B4%29%5E2=144 ALIGN=MIDDLE  ALT=\"4x%5E2%2B9%28-2x%2F3%2B4%29%5E2=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B9%28%284%2F9%29x%5E2-16x%2F3%2B16%29=144 ALIGN=MIDDLE  ALT=\"4x%5E2%2B9%28%284%2F9%29x%5E2-16x%2F3%2B16%29=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B4x%5E2-3%2A16x%2B9%2A16=144 ALIGN=MIDDLE  ALT=\"4x%5E2%2B4x%5E2-3%2A16x%2B9%2A16=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2-48x%2B151=144 ALIGN=MIDDLE  ALT=\"8x%5E2-48x%2B151=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2-48x%2B7=0 ALIGN=MIDDLE  ALT=\"8x%5E2-48x%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Discriminant:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-48%29%5E2-4%2A8%2A7=2080 ALIGN=MIDDLE  ALT=\"%28-48%29%5E2-4%2A8%2A7=2080\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factoring Discriminant:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=208%2A10=104%2A2%2A10=52%2A2%2A2%2A10=4%2A13%2A2%2A2%2A2%2A10=2%5E5%2A13%2A2%2A5=2%5E6%2A5%2A13 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Continuing with general solution of quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2848%2B-+sqrt%282%5E6%2A5%2A13%29%29%2F%282%2A8%29 ALIGN=MIDDLE  ALT=\"x=%2848%2B-+sqrt%282%5E6%2A5%2A13%29%29%2F%282%2A8%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=%2848%2B-+8sqrt%2865%29%29%2F%282%2A8%29 ALIGN=MIDDLE  ALT=\"x=%2848%2B-+8sqrt%2865%29%29%2F%282%2A8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=%286%2B-+sqrt%2865%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=%286%2B-+sqrt%2865%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for the two x coordinates.\r<BR>\n" );
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document.write( "FINDING y COORDINATES<BR>\n" );
document.write( "Found from earlier, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2F3%2B4 ALIGN=MIDDLE  ALT=\"y=-2x%2F3%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%282%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y=-%282%2F3%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%282%2F3%29%28%286%2B-+sqrt%2865%29%29%2F2%29%2B4 ALIGN=MIDDLE  ALT=\"y=-%282%2F3%29%28%286%2B-+sqrt%2865%29%29%2F2%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4%2B-+%281%2F3%29sqrt%2865%29%2B4 ALIGN=MIDDLE  ALT=\"y=-4%2B-+%281%2F3%29sqrt%2865%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, notice the resulting additive inverses 4 and -4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%281%2F3%29sqrt%2865%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%281%2F3%29sqrt%2865%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%281%2F3%29sqrt%2865%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%281%2F3%29sqrt%2865%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Careful which coordinate goes with which other coordiante.<BR>\n" );
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document.write( "x,y:    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-sqrt%2865%29%2F2 ALIGN=MIDDLE  ALT=\"6-sqrt%2865%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2865%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%2865%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x,y:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Bsqrt%2865%29%2F2 ALIGN=MIDDLE  ALT=\"6%2Bsqrt%2865%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2865%29%2F3 ALIGN=MIDDLE  ALT=\"-sqrt%2865%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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