document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983071>Question 983071</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations\r<BR>\n" );
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document.write( "x^2 + y^2 - x - y = 18<BR>\n" );
document.write( "xy + 2x + 2y = 26\r<BR>\n" );
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document.write( "I'm really having hard time at this part. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603890 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "You need to solve the non-linear system of two equations in two unknowns\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2+%2B+y%5E2+-+x+-+y+=+18%2C%0D%0Axy+%2B+2x+%2B+2y+=+26%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2+%2B+y%5E2+-+x+-+y+=+18%2C%0D%0Axy+%2B+2x+%2B+2y+=+26%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Multiply the second equation by &nbsp;2 &nbsp;(both sides)&nbsp; and then add to the first one. &nbsp;You will get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2xy+%2B+y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2xy+%2B+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28x%2By%29 ALIGN=MIDDLE  ALT=\"3%2A%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+%2B+2%2A26 ALIGN=MIDDLE  ALT=\"18+%2B+2%2A26\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  &nbsp;&nbsp;or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+y%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+%2B+y%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28x%2By%29 ALIGN=MIDDLE  ALT=\"3%2A%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70 ALIGN=MIDDLE  ALT=\"70\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.\r<BR>\n" );
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document.write( "The last equation is quadratic for &nbsp;(x + y)&nbsp; and has the roots\r<BR>\n" );
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document.write( "a) x + y = -10   &nbsp;&nbsp;and &nbsp;&nbsp;b) x + y = 7.\r<BR>\n" );
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document.write( "So, &nbsp;combining this with the second equation of the original system, you should solve two systems\r<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x+%2B+y+=+-10%2C%0D%0Axy+%2B+2%2A%28-10%29+=+26%29 ALIGN=MIDDLE  ALT=\"system%28x+%2B+y+=+-10%2C%0D%0Axy+%2B+2%2A%28-10%29+=+26%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;&nbsp;&nbsp;&nbsp;and &nbsp;&nbsp;&nbsp;&nbsp;b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x+%2B+y+=+7%2C%0D%0Axy+%2B+2%2A7+=+26%29 ALIGN=MIDDLE  ALT=\"system%28x+%2B+y+=+7%2C%0D%0Axy+%2B+2%2A7+=+26%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "or \r<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x+%2B+y+=+-10%2C%0D%0Axy+=+46%29 ALIGN=MIDDLE  ALT=\"system%28x+%2B+y+=+-10%2C%0D%0Axy+=+46%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;&nbsp;&nbsp;&nbsp;and &nbsp;&nbsp;&nbsp;&nbsp;b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x+%2B+y+=+7%2C%0D%0Axy+=+40%29 ALIGN=MIDDLE  ALT=\"system%28x+%2B+y+=+7%2C%0D%0Axy+=+40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The system &nbsp;a)&nbsp; has no real solutions. \r<BR>\n" );
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document.write( "The system &nbsp;b)&nbsp; has two solutions &nbsp;x=4, y=3 &nbsp;and &nbsp;x=3, y=4. \r<BR>\n" );
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document.write( "<B>Answer</B>. &nbsp;Two solutions are &nbsp;x=4, y=3 &nbsp;and &nbsp;x=3, y=4. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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