document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224914>Question 224914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve this simultaneous equation: \r<BR>\n" );
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document.write( "x+y=10<BR>\n" );
document.write( "y=3x²-2x-3\r<BR>\n" );
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document.write( "I have tried every way i can think of to solve this equation but i have failed. Please help me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167966 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve this simultaneous equation: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=10 ALIGN=MIDDLE  ALT=\"x%2By=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%5E2-2x-3 ALIGN=MIDDLE  ALT=\"y=3x%5E2-2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Equation 2\r<BR>\n" );
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document.write( "Step 1.  In Equation 1, solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10-x ALIGN=MIDDLE  ALT=\"y=10-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute y into Equation 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-x=3x%5E2-2x-3 ALIGN=MIDDLE  ALT=\"10-x=3x%5E2-2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2.  Add x-10 to both sides of the equatiion\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-x%2Bx-10=3x%5E2-2x-3%2Bx-10 ALIGN=MIDDLE  ALT=\"10-x%2Bx-10=3x%5E2-2x-3%2Bx-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3x%5E2-x-13 ALIGN=MIDDLE  ALT=\"0=3x%5E2-x-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3.  To solve use the quadratic formula given below:\r<BR>\n" );
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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;\" > \r<BR>\n" );
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document.write( "where a=3, b=-1, and c=-13\r<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=quadratic.solver>SOLVE quadratic equation with variable</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-1x%2B-13+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-1x%2B-13+=+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" );
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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=%28-1%29%5E2-4%2A3%2A-13=157 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1%29%5E2-4%2A3%2A-13=157\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=157 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--1%2B-sqrt%28+157+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1%2B-sqrt%28+157+%29%29%2F2%5Ca\"   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=x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+157+%29%29%2F2%5C3+=+2.25499401435694 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+157+%29%29%2F2%5C3+=+2.25499401435694\"   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-%28-1%29-sqrt%28+157+%29%29%2F2%5C3+=+-1.92166068102361 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-1%29-sqrt%28+157+%29%29%2F2%5C3+=+-1.92166068102361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-1x%2B-13 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-1x%2B-13\"   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-1x%2B-13+=+3%28x-2.25499401435694%29%2A%28x--1.92166068102361%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-1x%2B-13+=+3%28x-2.25499401435694%29%2A%28x--1.92166068102361%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.25499401435694, -1.92166068102361.\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-1%2Ax%2B-13+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1%2Ax%2B-13+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Step 4.  Now, for each value of x found in Step 3, substitute into y=10-x to get two values for y.\r<BR>\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( " </SPAN>\n" );
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