document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167729>Question 167729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I dont know where to start.\r<BR>\n" );
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document.write( "Please help me in solving this question\r<BR>\n" );
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document.write( "Simultaneous equation\r<BR>\n" );
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document.write( "3x-4y=5<BR>\n" );
document.write( "3x^2-xy-3y^2=21<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123672 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=123672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simultaneous equation <BR>\n" );
document.write( "3x-4y=5<BR>\n" );
document.write( "3x^2-xy-3y^2=21<BR>\n" );
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document.write( "Solve the 1 eqn for y<BR>\n" );
document.write( "3x-4y=5<BR>\n" );
document.write( "-4y = 5-3x<BR>\n" );
document.write( "y = (3/4)x - 5/4<BR>\n" );
document.write( "Sub for y into the 2nd eqn<BR>\n" );
document.write( "3x^2 - x*((3/4)x - 5/4) - 3*((3/4)x - 5/4)^2 = 21<BR>\n" );
document.write( "Now it's all in x<BR>\n" );
document.write( "3x^2 - (3/4)x^2 + 5x/4 - 3*((9/16)x^2 - 15x/8 + 25/16 = 21<BR>\n" );
document.write( "Multiply by 16<BR>\n" );
document.write( "48x^2 - 12x^2 + 20x - 27x^2 + 90x - 75 = 336<BR>\n" );
document.write( "9x^2 + 110x - 261 = 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=9x%5E2%2B110x%2B-411+=+0 ALIGN=MIDDLE  ALT=\"9x%5E2%2B110x%2B-411+=+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=%28110%29%5E2-4%2A9%2A-411=26896 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28110%29%5E2-4%2A9%2A-411=26896\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=26896 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+=+%28-110%2B-sqrt%28+26896+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-110%2B-sqrt%28+26896+%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-%28110%29%2Bsqrt%28+26896+%29%29%2F2%5C9+=+3 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28110%29%2Bsqrt%28+26896+%29%29%2F2%5C9+=+3\"   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-%28110%29-sqrt%28+26896+%29%29%2F2%5C9+=+-15.2222222222222 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28110%29-sqrt%28+26896+%29%29%2F2%5C9+=+-15.2222222222222\"   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=9x%5E2%2B110x%2B-411 ALIGN=MIDDLE  ALT=\"9x%5E2%2B110x%2B-411\"   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=9x%5E2%2B110x%2B-411+=+%28x-3%29%2A%28x--15.2222222222222%29 ALIGN=MIDDLE  ALT=\"9x%5E2%2B110x%2B-411+=+%28x-3%29%2A%28x--15.2222222222222%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3, -15.2222222222222.\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+9%2Ax%5E2%2B110%2Ax%2B-411+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B110%2Ax%2B-411+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "x = 3, y = 1<BR>\n" );
document.write( "x = -15 2/9, y = -38/3\r<BR>\n" );
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