document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=499019>Question 499019</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please tell me how I would graph this. The question is:<BR>\n" );
document.write( "Graph the solution set of the following system of inequalities:<BR>\n" );
document.write( "x^2+y^2 less than or equal to 25<BR>\n" );
document.write( "y greater than or equal to |x| </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #337339 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=337339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to graph them, you make the inequality an equality and then you solve for y.<BR>\n" );
document.write( "y >= |x| becomes y = |x|.<BR>\n" );
document.write( "you can graph it as such.<BR>\n" );
document.write( "x^2 + y^2 <= 25 becomes x^2 + y^2 = 25<BR>\n" );
document.write( "subtract x^2 from both sides of the equation to get y^2 = 25 - x^2<BR>\n" );
document.write( "take the square root of both sides of the equation to get y = +/- sqrt(25 - x^2)<BR>\n" );
document.write( "you can graph it as such.<BR>\n" );
document.write( "the equations you are graphing are:<BR>\n" );
document.write( "y = |x|<BR>\n" );
document.write( "y = +/- sqrt(25-x^2)<BR>\n" );
document.write( "your graph will look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2011/sep161.jpg\" alt = \"$$$$$\" /><BR>\n" );
document.write( "now you have to go back to the inequality and figure out which part of this graph is what you want.<BR>\n" );
document.write( "we'll start with y >= |x|<BR>\n" );
document.write( "if x is positive, then this is equivalent to y >= x.<BR>\n" );
document.write( "if x is negative, then this is equivalent to y >= -x.<BR>\n" );
document.write( "regardless of whether x is positive or negative, y will always be positive.<BR>\n" );
document.write( "in both cases the value of y will be on the line of the graph or above it.<BR>\n" );
document.write( "next we'll work on x^2 + y^2 <= 25<BR>\n" );
document.write( "we subtract x^2 from both sides of the equation to get:<BR>\n" );
document.write( "y^2 <= 25 - x^2<BR>\n" );
document.write( "we take the square root of both sides of this equation to get:<BR>\n" );
document.write( "y <= sqrt(25 - x^2) and y >= -sqrt(25 - x^2)<BR>\n" );
document.write( "this may be a little hard to see, but it has to be this way in order for y^2 to be smaller than or equal to 25 - x^2.<BR>\n" );
document.write( "in our example, we are only concerned with y <= sqrt(x) because we are restricted to positive values of y since y has to be >= |x|.<BR>\n" );
document.write( "the shaded area in the graph shows you the area of the graph that is compatible with the requirements of the problem.<BR>\n" );
document.write( "y >= |x| puts y above the graph of that equation.<BR>\n" );
document.write( "y <= sqrt(25 - x^2) puts y within the boundaries of the circle.\r<BR>\n" );
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