document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145021>Question 145021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with 2 homework problems.  I can use any method (elimination, subtitution or graphical methods) the problems are  5x + 6y = 14<BR>\n" );
document.write( "                                                    -3y + x = 7 I got (35/12, -7/12)\r<BR>\n" );
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document.write( "next problem 2x/3 +  3y/4  =  11/12\r<BR>\n" );
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document.write( "        x/3  +  7y/18 =  1/2    <BR>\n" );
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document.write( "(I got (8/5, -3/35) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105727 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=105727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "Start with the given system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%285x%2B6y=14%2Cx-3y=7%29 ALIGN=MIDDLE  ALT=\"system%285x%2B6y=14%2Cx-3y=7%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=1%285x%2B6y%29=1%2814%29 ALIGN=MIDDLE  ALT=\"1%285x%2B6y%29=1%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the top equation (both sides) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%28x-3y%29=-5%287%29 ALIGN=MIDDLE  ALT=\"-5%28x-3y%29=-5%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the bottom equation (both sides) by <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( "Distribute and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%2B15y=-35 ALIGN=MIDDLE  ALT=\"-5x%2B15y=-35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. In order to add 2 equations, group like terms and combine them\r<BR>\n" );
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document.write( "Combine like terms and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%285x-5x%29%2B21y=-21 ALIGN=MIDDLE  ALT=\"cross%285x-5x%29%2B21y=-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice how the x terms cancel out\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21y=-21 ALIGN=MIDDLE  ALT=\"21y=-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-21%2F21 ALIGN=MIDDLE  ALT=\"y=-21%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Now plug this answer into the top equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6y=14 ALIGN=MIDDLE  ALT=\"5x%2B6y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6y=14 ALIGN=MIDDLE  ALT=\"5x%2B6y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6%28-1%29=14 ALIGN=MIDDLE  ALT=\"5x%2B6%28-1%29=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   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=5x-6=14 ALIGN=MIDDLE  ALT=\"5x-6=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=14%2B6 ALIGN=MIDDLE  ALT=\"5x=14%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 6 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=20 ALIGN=MIDDLE  ALT=\"5x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2820%29%2F%285%29 ALIGN=MIDDLE  ALT=\"x=%2820%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So our answer is\r<BR>\n" );
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document.write( "which also looks like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(4,-1\right)\">\r<BR>\n" );
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document.write( "Now let's graph the two equations (if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)\r<BR>\n" );
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document.write( "From the graph, we can see that the two equations intersect at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(4,-1\right)\">. This visually verifies our answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28500%2C+500%2C+-10%2C10%2C-10%2C10%2C%0D%0A++graph%28500%2C+500%2C+-10%2C10%2C-10%2C10%2C+%2814-5%2Ax%29%2F%286%29%2C+%287-1%2Ax%29%2F%28-3%29+%29%2C%0D%0A++blue%28circle%284%2C-1%2C0.1%29%29%2C%0D%0A++blue%28circle%284%2C-1%2C0.12%29%29%2C%0D%0A++blue%28circle%284%2C-1%2C0.15%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B6y=14 ALIGN=MIDDLE  ALT=\"5x%2B6y=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3y=7 ALIGN=MIDDLE  ALT=\"x-3y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)  and the intersection of the lines (blue circle).\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "Let's look at the first equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F3%2B3y%2F4=11%2F12 ALIGN=MIDDLE  ALT=\"2x%2F3%2B3y%2F4=11%2F12\"   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=12%282x%2Fcross%283%29%2B3y%2Fcross%284%29%29=12%2811%2Fcross%2812%29%29 ALIGN=MIDDLE  ALT=\"12%282x%2Fcross%283%29%2B3y%2Fcross%284%29%29=12%2811%2Fcross%2812%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides of the first equation by the LCD 12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B9y=11 ALIGN=MIDDLE  ALT=\"8x%2B9y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "---------\r<BR>\n" );
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document.write( "Let's look at the second equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F3%2B7y%2F18=1%2F2 ALIGN=MIDDLE  ALT=\"x%2F3%2B7y%2F18=1%2F2\"   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=18%28x%2Fcross%283%29%2B7y%2Fcross%2818%29%29=18%281%2Fcross%282%29%29 ALIGN=MIDDLE  ALT=\"18%28x%2Fcross%283%29%2B7y%2Fcross%2818%29%29=18%281%2Fcross%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides of the second equation by the LCD 18\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B7y=9 ALIGN=MIDDLE  ALT=\"6x%2B7y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "So our new system of equations is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%288x%2B9y%29=3%2811%29 ALIGN=MIDDLE  ALT=\"3%288x%2B9y%29=3%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the top equation (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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%286x%2B7y%29=-4%289%29 ALIGN=MIDDLE  ALT=\"-4%286x%2B7y%29=-4%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the bottom equation (both sides) by <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( "Distribute and multiply\r<BR>\n" );
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document.write( "Now add the equations together. In order to add 2 equations, group like terms and combine them\r<BR>\n" );
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document.write( "Combine like terms and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2824x-24x%29-y=-3 ALIGN=MIDDLE  ALT=\"cross%2824x-24x%29-y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice how the x terms cancel out\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y=-3 ALIGN=MIDDLE  ALT=\"-y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2F-1 ALIGN=MIDDLE  ALT=\"y=-3%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Now plug this answer into the top equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B9y=11 ALIGN=MIDDLE  ALT=\"8x%2B9y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B9y=11 ALIGN=MIDDLE  ALT=\"8x%2B9y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B9%283%29=11 ALIGN=MIDDLE  ALT=\"8x%2B9%283%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=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=8x%2B27=11 ALIGN=MIDDLE  ALT=\"8x%2B27=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=11-27 ALIGN=MIDDLE  ALT=\"8x=11-27\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 27 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=-16 ALIGN=MIDDLE  ALT=\"8x=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-16%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x=%28-16%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 8 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So our answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which also looks like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-2,3\right)\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );