document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=349538>Question 349538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Part 1: <BR>\n" );
document.write( "Suppose you need to solve a system of equations in which one equation represents a circle and the other represents a line.  How many solutions can your system have?  Select ALL that are possible. \r<BR>\n" );
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document.write( "0,1,2,3,4, infinitely many\r<BR>\n" );
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document.write( "Part 2:<BR>\n" );
document.write( "How many solutions does the following system of equations have? <BR>\n" );
document.write( "x2+y2=64<BR>\n" );
document.write( "x=1\r<BR>\n" );
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document.write( "0,1,2,3,4, infinitely many </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #249827 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=249827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> one equation represents a circle and the other equation represents a line.\r<BR>\n" );
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document.write( "you can have 0, 1, or 2 solutions.\r<BR>\n" );
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document.write( "0 if the line and the circle never intersect<BR>\n" );
document.write( "1 if the line is tangent to the circle.<BR>\n" );
document.write( "2 if the line intersects the circle at any other angle.\r<BR>\n" );
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document.write( "the line can never intersect the circle at more than 2 points.\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "x^2 + y^2 = 64<BR>\n" );
document.write( "x = 1\r<BR>\n" );
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document.write( "this is like solving equations simultaneously to get a common solution.\r<BR>\n" );
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document.write( "if x = 1, you can substitute in the first equation to get 1 + y^2 = 64 which give you y^2 = 63 which gives you y = +/- sqrt(63).\r<BR>\n" );
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document.write( "this implies 2 solutions to this equation.\r<BR>\n" );
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document.write( "The graph of the equation of the circle should confirm this.\r<BR>\n" );
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document.write( "To graph the equation of the circle, solve for y to get:\r<BR>\n" );
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document.write( "y = +/- sqrt(64-x^2)\r<BR>\n" );
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document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Csqrt%2864-x%5E2%29%2C-sqrt%2864-x%5E2%29%2C7.937253933%2C-7.937253933%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Draw a vertical line at x = 1 and you will see that the intersection of that vertical line and the circle is around y = +/- 7.937253933.\r<BR>\n" );
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document.write( "I drew 2 horizontal lines at y = +/- 7.937253933 so you can see that a little easier.\r<BR>\n" );
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document.write( "when x = 0, y = +/- sqrt(64-0) = +/- sqrt(64) = +/- 8.\r<BR>\n" );
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document.write( "That's the highest and lowest point of the circle.\r<BR>\n" );
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document.write( "when x = 1, y = +/- sqrt(64-1) = +/- sqrt(63) = +/- 7.937253933.  \r<BR>\n" );
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document.write( "That's close to the highest point but hot exactly there (just a little below).\r<BR>\n" );
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document.write( "Solving the 2 equations simultaneously yielded the result.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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