document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316866>Question 316866</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is an example when the solution of a system of inequalities must be in the first quadrant?  Why is it constrained to this quadrant?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I know that in order for a solution of a system of inequalities to be in the forst quadrant it must be a positive number. But how do I show an example? Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226807 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=226807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the solution has to be in the first quadrant then the value of y and the value of x have to be in the first quadrant.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An equation like y > sqrt(x) should satisfy this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A graph of this equation would look like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Csqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Csqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x is negative, x is undefined, so the domain of this function has to be all values of x >= 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since all values of x are >= 0, then y = sqrt(x) must be positive as well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If y has to be greater than sqrt(x), then the equation y > sqrt(x) will be all values of y that are above the graph of the equation y = sqrt(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This has isolated both x and y to be greater than or equal to 0 which conforms to the requirement that the solution is in quadrant 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I think that's what they mean.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You have to select a domain that can only be positive and then create an equation where the value of y will also always be positive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An equation where this would not work would be y > absolute value of x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The graph of that equation looks like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cabs%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cabs%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can see from this graph, that while the value of y is always positive, the value of x can also be negative which places the solution in both quadrants 1 and 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In quadrant 1 both x and y are positive<BR>\n" );
document.write( "In quadrant 2, x is negative and y is positive<BR>\n" );
document.write( "In quadrant 3, both x and y are negative<BR>\n" );
document.write( "In quadrant 4, x is positive and y is negative<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );