document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980038>Question 980038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the line containing the centers of the two circles: <BR>\n" );
document.write( "x² + y² - 10x - 10y + 49 = 0 and x² + y² - 4x - 6y + 9 = 0.<BR>\n" );
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document.write( "a. -2x - 3y + 5 = 0<BR>\n" );
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document.write( "b. 2x + 3y + 5 = 0<BR>\n" );
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document.write( "c. 8x - 7y + 5 = 0<BR>\n" );
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document.write( "d. 2x - 3y + 5 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601242 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601242\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> an equation of the line containing the centers of the two circles: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+-+10x+-+10y+%2B+49+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+-+10x+-+10y+%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...........complete squares and write equation of a circle in a form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+10x%2Bb%5E2%29+-b%5E2%2B+%28y%5E2+-+10y%2Bb%5E2%29+-b%5E2%2B+49+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+10x%2Bb%5E2%29+-b%5E2%2B+%28y%5E2+-+10y%2Bb%5E2%29+-b%5E2%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "....recall, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in your case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+10x%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+10x%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=10 ALIGN=MIDDLE  ALT=\"2ab=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=10 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=10 ALIGN=MIDDLE  ALT=\"2b=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5 ALIGN=MIDDLE  ALT=\"b=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we can write\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+10x%2B5%5E2%29+-5%5E2%2B+%28y%5E2+-+10y%2B5%5E2%29+-5%5E2%2B+49+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+10x%2B5%5E2%29+-5%5E2%2B+%28y%5E2+-+10y%2B5%5E2%29+-5%5E2%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+5%29%5E2+-25%2B+%28y+-+5%29%5E2+-25%2B+49+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+5%29%5E2+-25%2B+%28y+-+5%29%5E2+-25%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+5%29%5E2+%2B+%28y+-+5%29%5E2+-50%2B+49+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+5%29%5E2+%2B+%28y+-+5%29%5E2+-50%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+5%29%5E2+%2B+%28y+-+5%29%5E2+-1+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+5%29%5E2+%2B+%28y+-+5%29%5E2+-1+=+0\"   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=%28x+-+5%29%5E2+%2B+%28y+-+5%29%5E2++=+1 ALIGN=MIDDLE  ALT=\"%28x+-+5%29%5E2+%2B+%28y+-+5%29%5E2++=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=5 ALIGN=MIDDLE  ALT=\"h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the center is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "now do same with other circle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+-+4x+-+6y+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+-+4x+-+6y+%2B+9+=+0\"   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=%28x%5E2++-+4x%2Bb%5E2%29-b%5E2%2B+%28y%5E2+-+6y+%2Bb%5E2%29-b%5E2%2B+9+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2++-+4x%2Bb%5E2%29-b%5E2%2B+%28y%5E2+-+6y+%2Bb%5E2%29-b%5E2%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=4 ALIGN=MIDDLE  ALT=\"2ab=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=4 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=6 ALIGN=MIDDLE  ALT=\"2ab=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=6 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   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=%28x%5E2++-+4x%2B2%5E2%29-2%5E2%2B+%28y%5E2+-+6y+%2B3%5E2%29-3%5E2%2B+9+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2++-+4x%2B2%5E2%29-2%5E2%2B+%28y%5E2+-+6y+%2B3%5E2%29-3%5E2%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x++-+2%29%5E2-4%2B+%28y+-+3%29%5E2-9%2B+9+=+0 ALIGN=MIDDLE  ALT=\"%28x++-+2%29%5E2-4%2B+%28y+-+3%29%5E2-9%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x++-+2%29%5E2%2B+%28y+-+3%29%5E2-4+=+0 ALIGN=MIDDLE  ALT=\"%28x++-+2%29%5E2%2B+%28y+-+3%29%5E2-4+=+0\"   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=%28x++-+2%29%5E2%2B+%28y+-+3%29%5E2=+4 ALIGN=MIDDLE  ALT=\"%28x++-+2%29%5E2%2B+%28y+-+3%29%5E2=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2 ALIGN=MIDDLE  ALT=\"h=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2 ALIGN=MIDDLE  ALT=\"r=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the center is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "now we have two points, (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and we can find the equation of a line passing through these two points\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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=change_this_name10094.solver>Find the equation of line going through points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (5, 5) and (x2, y2) = (2, 3).<BR>\n" );
document.write( "  Slope a is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%283-5%29%2F%282-5%29+=+0.666666666666667 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  Intercept is found from equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5B1%5D%2Bb+=+y%5B1%5D ALIGN=MIDDLE  ALT=\"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.666666666666667%2A5+%2Bb+=+1.66666666666667 ALIGN=MIDDLE  ALT=\"0.666666666666667%2A5+%2Bb+=+1.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From that, <BR>\n" );
document.write( "  intercept b is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5-0.666666666666667%2A5+=+1.66666666666667 ALIGN=MIDDLE  ALT=\"b=5-0.666666666666667%2A5+=+1.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  y=(0.666666666666667)x + (1.66666666666667)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Your graph:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C%0D%0A++++graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+0.666666666666667%2Ax%2B1.66666666666667+%29%2C%0D%0A++++red%28+locate%28+5%2C+5%2C+%225%2C+5%22+%29%2C+circle%28+5%2C+5%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+2%2C+3%2C+%222%2C+3%22+%29%2C+circle%28+2%2C+3%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "since your line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.666666666666667x+%2B+1.66666666666667 ALIGN=MIDDLE  ALT=\"y=0.666666666666667x+%2B+1.66666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x+%2B+5%2F3 ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x+%2B+5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=3%282%2F3%29x+%2B+3%285%2F3%29 ALIGN=MIDDLE  ALT=\"3y=3%282%2F3%29x+%2B+3%285%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=2x+%2B+5 ALIGN=MIDDLE  ALT=\"3y=2x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, in standard form will be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y%2B5=0 ALIGN=MIDDLE  ALT=\"2x-3y%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your answer is:\r<BR>\n" );
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document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+3y+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"2x+-+3y+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%285%2C5%2C.12%29%2Ccircle%285%2C5%2C1%29%2Ccircle%282%2C3%2C2%29%2Ccircle%282%2C3%2C.12%29%2C%0D%0Alocate%285%2C5%2CC%285%2C5%29%29%2Clocate%282%2C3%2CC%282%2C3%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2F3+%2B+5%2F3%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );