document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=435200>Question 435200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you sovle the system x^2=25-y^2 and xy=-12 algebarically? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301274 by </B><A HREF=/tutors/aboutme.mpl?userid=Gogonati><B>Gogonati(855)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Gogonati><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=Gogonati><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=301274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2%2By%5E2=25%2C+x%2Ay=-12%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2%2By%5E2=25%2C+x%2Ay=-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, first we make some identical \r<BR>\n" );
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document.write( "transformations in the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B2xy=25%2B2xy ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B2xy=25%2B2xy\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E2=25%2B2%28-12%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E2=25%2B2%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=1 ALIGN=MIDDLE  ALT=\"x%2By=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=-1 ALIGN=MIDDLE  ALT=\"x%2By=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we need to solve two other simplest systems:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=1%2C+x%2Ay=-12%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=1%2C+x%2Ay=-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=-1%2C+x%2Ay=-12%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=-1%2C+x%2Ay=-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We  solve these systems by substitution:1) y=1-x and x(1-x)=-12 =>-x^2+x+12=0, where x=4 and x=-3.\r<BR>\n" );
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document.write( "Plug in x=4  we get y=-3 and plug in x=-3 we get y=4<BR>\n" );
document.write( "We got two solution: (4, -3) and (-3, 4)\r<BR>\n" );
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document.write( "2)y=-x-1 and x(-x-1)=-12 => -x^2-x+12=0, where x=3 and x=-4<BR>\n" );
document.write( "Plug in x=3 we get y=-4 and plug in x=-4 we get y=3 and we get two other solutions: (3, -4) and (-4, 3). Summarize the results we :\r<BR>\n" );
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document.write( "Answer:The solution are the points: (4, -3), (-3, 4), (3, -4) and ( -4, 3).<BR>\n" );
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