document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200186>Question 1200186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of a curve xy = 12 and the equation of a line L is 2x + y = k, where k is<BR>\n" );
document.write( "a constant.<BR>\n" );
document.write( "i) In the case where k = 11, find the coordinates of the points of intersction of L<BR>\n" );
document.write( "and the curve.<BR>\n" );
document.write( "ii) Find the set of values of & for which I does not intersect the curve. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834246 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll answer part (i) only. <BR>\n" );
document.write( "Part (ii) seems a bit garbled so you'll need to revise.\r<BR>\n" );
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document.write( "Part (i)\r<BR>\n" );
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document.write( "Plug k = 11 into the 2nd equation and isolate y.<BR>\n" );
document.write( "2x+y = k<BR>\n" );
document.write( "2x+y = 11<BR>\n" );
document.write( "y = -2x+11\r<BR>\n" );
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document.write( "Plug this into the other equation.<BR>\n" );
document.write( "xy = 12<BR>\n" );
document.write( "x(-2x+11) = 12<BR>\n" );
document.write( "-2x^2+11x = 12<BR>\n" );
document.write( "-2x^2+11x-12 = 0\r<BR>\n" );
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document.write( "Turn to the quadratic formula.<BR>\n" );
document.write( "We'll plug in <BR>\n" );
document.write( "a = -2<BR>\n" );
document.write( "b = 11<BR>\n" );
document.write( "c = -12<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%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=x+=+%28-11%2B-sqrt%28%2811%29%5E2-4%28-2%29%28-12%29%29%29%2F%282%28-2%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11%2B-sqrt%28%2811%29%5E2-4%28-2%29%28-12%29%29%29%2F%282%28-2%29%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=x+=+%28-11%2B-sqrt%28121+-+96%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11%2B-sqrt%28121+-+96%29%29%2F%28-4%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=x+=+%28-11%2B-sqrt%2825%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11%2B-sqrt%2825%29%29%2F%28-4%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=x+=+%28-11%2B-++5%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11%2B-++5%29%2F%28-4%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=x+=+%28-11%2B5%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11%2B5%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-11-5%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-11-5%29%2F%28-4%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=x+=+%28-6%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-16%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16%29%2F%28-4%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=x+=+3%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.5 ALIGN=MIDDLE  ALT=\"x+=+1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <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;\" >\r<BR>\n" );
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document.write( "If x = 1.5, then,<BR>\n" );
document.write( "y = -2x+11<BR>\n" );
document.write( "y = -2*1.5+11<BR>\n" );
document.write( "y = -3+11<BR>\n" );
document.write( "y = 8<BR>\n" );
document.write( "Making (1.5, 8) one point of intersection.\r<BR>\n" );
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document.write( "If x = 4, then,<BR>\n" );
document.write( "y = -2x+11<BR>\n" );
document.write( "y = -2*4+11<BR>\n" );
document.write( "y = -8+11<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "Making (4, 3) the other point of intersection.\r<BR>\n" );
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document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-3%2C10%2C-3%2C10%2C%0D%0Agraph%28400%2C400%2C-3%2C10%2C-3%2C10%2C-100%2C12%2Fx%2C-2x%2B11%29%2C%0D%0Acircle%281.5%2C8%2C0.02%29%2C%0D%0Acircle%281.5%2C8%2C0.04%29%2C%0D%0Acircle%281.5%2C8%2C0.06%29%2C%0D%0Acircle%281.5%2C8%2C0.08%29%2C%0D%0Acircle%281.5%2C8%2C0.10%29%2C%0D%0Acircle%281.5%2C8%2C0.12%29%2C%0D%0Acircle%281.5%2C8%2C0.14%29%2C%0D%0Acircle%281.5%2C8%2C0.16%29%2C%0D%0Acircle%281.5%2C8%2C0.18%29%2C%0D%0A%0D%0Acircle%284%2C3%2C0.02%29%2C%0D%0Acircle%284%2C3%2C0.04%29%2C%0D%0Acircle%284%2C3%2C0.06%29%2C%0D%0Acircle%284%2C3%2C0.08%29%2C%0D%0Acircle%284%2C3%2C0.10%29%2C%0D%0Acircle%284%2C3%2C0.12%29%2C%0D%0Acircle%284%2C3%2C0.14%29%2C%0D%0Acircle%284%2C3%2C0.16%29%2C%0D%0Acircle%284%2C3%2C0.18%29%2C%0D%0A%0D%0Alocate%281.5%2B0.5%2C8%2B0.5%2C%22%281.5%2C8%29%22%29%2C%0D%0Alocate%284%2B0.5%2C3%2B0.5%2C%22%284%2C3%29%22%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "xy = 12 in green<BR>\n" );
document.write( "2x+y = k in blue, where k = 11<BR>\n" );
document.write( "1.5 = 3/2\r<BR>\n" );
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document.write( "Here's a more zoomed-out look of the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-100%2C12%2Fx%2C-2x%2B11%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I recommend using either Desmos or GeoGebra as a graphing tool. <BR>\n" );
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