document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203724>Question 203724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations:\r<BR>\n" );
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document.write( "x^2 + 4y^2=4<BR>\n" );
document.write( "(x-1)^2+y^2=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153742 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=153742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 + 4y^2=4  --> 4y^2 = 4 - x^2<BR>\n" );
document.write( "(x-1)^2+y^2=1 --> 4x^2 - 8x + 4 + 4y^2 = 4<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Sub for 4y^2 into 2nd eqn<BR>\n" );
document.write( "4x^2 - 8x + 4 + (4-x^2) = 4<BR>\n" );
document.write( "3x^2 - 8x + 4 = 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=3x%5E2%2B-8x%2B4+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-8x%2B4+=+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=%28-8%29%5E2-4%2A3%2A4=16 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-8%29%5E2-4%2A3%2A4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=16 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--8%2B-sqrt%28+16+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--8%2B-sqrt%28+16+%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-%28-8%29%2Bsqrt%28+16+%29%29%2F2%5C3+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+16+%29%29%2F2%5C3+=+2\"   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-%28-8%29-sqrt%28+16+%29%29%2F2%5C3+=+0.666666666666667 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-8%29-sqrt%28+16+%29%29%2F2%5C3+=+0.666666666666667\"   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=3x%5E2%2B-8x%2B4 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-8x%2B4\"   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=3x%5E2%2B-8x%2B4+=+%28x-2%29%2A%28x-0.666666666666667%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-8x%2B4+=+%28x-2%29%2A%28x-0.666666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2, 0.666666666666667.\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+3%2Ax%5E2%2B-8%2Ax%2B4+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-8%2Ax%2B4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "x = 2<BR>\n" );
document.write( "x = 2/3<BR>\n" );
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document.write( "at x=2: y = 0<BR>\n" );
document.write( "--> (2,0) One solution<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "at x = 2/3: y = +/- sqrt(8)/3<BR>\n" );
document.write( "--> (2/3,y) 2nd point/solution<BR>\n" );
document.write( "--> (2/3,-y) 3rd point/solution<BR>\n" );
document.write( "---------------------------- </SPAN>\n" );
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