document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200162>Question 200162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi!\r<BR>\n" );
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document.write( "Use the substitution method to find all solutions of the system of equations. (Round each answer to two decimal places.)\r<BR>\n" );
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document.write( "{2x^2+4y=11<BR>\n" );
document.write( " x^2-y^2=1/2\r<BR>\n" );
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document.write( "thanks for the homework help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150459 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=150459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2=1%2F2 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1%2F2%2By%5E2 ALIGN=MIDDLE  ALT=\"x%5E2=1%2F2%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4y=11 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%281%2F2%2By%5E2%29%2B4y=11 ALIGN=MIDDLE  ALT=\"2%281%2F2%2By%5E2%29%2B4y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1%2F2%2By%5E2 ALIGN=MIDDLE  ALT=\"x%5E2=1%2F2%2By%5E2\"   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=2%2B2y%5E2%2B4y=11 ALIGN=MIDDLE  ALT=\"2%2B2y%5E2%2B4y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B2y%5E2%2B4y-11=0 ALIGN=MIDDLE  ALT=\"2%2B2y%5E2%2B4y-11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 11 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2%2B4y-9=0 ALIGN=MIDDLE  ALT=\"2y%5E2%2B4y-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2%2B4y-9 ALIGN=MIDDLE  ALT=\"2y%5E2%2B4y-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ay%5E2%2BBy%2BC ALIGN=MIDDLE  ALT=\"Ay%5E2%2BBy%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2 ALIGN=MIDDLE  ALT=\"A=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=4 ALIGN=MIDDLE  ALT=\"B=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-9 ALIGN=MIDDLE  ALT=\"C=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"y\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%282%29%28-9%29+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%282%29%28-9%29+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2 ALIGN=MIDDLE  ALT=\"A=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=4 ALIGN=MIDDLE  ALT=\"B=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-9 ALIGN=MIDDLE  ALT=\"C=-9\"   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=y+=+%28-4+%2B-+sqrt%28+16-4%282%29%28-9%29+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28-4+%2B-+sqrt%28+16-4%282%29%28-9%29+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   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=y+=+%28-4+%2B-+sqrt%28+16--72+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28-4+%2B-+sqrt%28+16--72+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%282%29%28-9%29 ALIGN=MIDDLE  ALT=\"4%282%29%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-72 ALIGN=MIDDLE  ALT=\"-72\"   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=y+=+%28-4+%2B-+sqrt%28+16%2B72+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28-4+%2B-+sqrt%28+16%2B72+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816--72%29 ALIGN=MIDDLE  ALT=\"sqrt%2816--72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2B72%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B72%29\"   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=y+=+%28-4+%2B-+sqrt%28+88+%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28-4+%2B-+sqrt%28+88+%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72 ALIGN=MIDDLE  ALT=\"72\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=88 ALIGN=MIDDLE  ALT=\"88\"   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=y+=+%28-4+%2B-+sqrt%28+88+%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y+=+%28-4+%2B-+sqrt%28+88+%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=y+=+%28-4+%2B-+2%2Asqrt%2822%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y+=+%28-4+%2B-+2%2Asqrt%2822%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-4%2B2%2Asqrt%2822%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y+=+%28-4%2B2%2Asqrt%2822%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-4-2%2Asqrt%2822%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y+=+%28-4-2%2Asqrt%2822%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2%2Bsqrt%2822%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2%2Bsqrt%2822%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2-sqrt%2822%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2-sqrt%2822%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the solutions (for \"y\") are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2%2Bsqrt%2822%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2%2Bsqrt%2822%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2-sqrt%2822%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2-sqrt%2822%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.35 ALIGN=MIDDLE  ALT=\"y=1.35\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3.35 ALIGN=MIDDLE  ALT=\"y=-3.35\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now plug these values into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1%2F2%2By%5E2 ALIGN=MIDDLE  ALT=\"x%5E2=1%2F2%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the corresponding \"x\" values. \r<BR>\n" );
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document.write( "Note: You should get four ordered pair solutions (there are two x values for each y value you just found).<BR>\n" );
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