document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195571>Question 1195571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can I please have help with this, Thank you! \r<BR>\n" );
document.write( "\n" );
document.write( "On the grid, sketch the inequalities below and determine the solution region. \r<BR>\n" );
document.write( "\n" );
document.write( "y is greater than or equal to 0\r<BR>\n" );
document.write( "\n" );
document.write( "x is greater than or equal to 0\r<BR>\n" );
document.write( "\n" );
document.write( "y is less than or equal to x+2\r<BR>\n" );
document.write( "\n" );
document.write( "y is less than or equal to 14-2x <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828102 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=828102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "We'll have these boundary equations<BR>\n" );
document.write( "y = 0<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "y = x+2<BR>\n" );
document.write( "y = -2x+14\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first two equations represent the x axis and y axis in that exact order. <BR>\n" );
document.write( "The last equation is equivalent to y = 14 - 2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Each equation mentioned is a solid line due to the \"or equal to\" as part of the inequality sign.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We're told that x ≥ 0 and y ≥ 0, which places us in the upper right quadrant. <BR>\n" );
document.write( "The shaded region is a subset of this quadrant. Meaning that the shaded region will not be found in any other quadrant.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To graph out y ≤ x+2, we will shade below the boundary equation y = x+2. This trick only works when y is fully isolated.<BR>\n" );
document.write( "Similarly, the graph of y ≤ -2x+14 will also be shaded below its corresponding boundary line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is what the final shaded region looks like when we overlap the four inequalities together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/PKVpNCA.png\"><BR>\n" );
document.write( "I used GeoGebra to make this graph. <BR>\n" );
document.write( "The input command I typed in was: <font color=red>( x >= 0) && (y >= 0) && (y <= x+2) && (y  <= -2x+14)</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Desmos is another tool you can use, and here's the link to the interactive graph:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.desmos.com/calculator/mkjjbdalpl\">https://www.desmos.com/calculator/mkjjbdalpl</a> <BR>\n" );
document.write( "This is what you would type in <font color=red>x >= 0 { y >= 0 } {y <= x+2} {y <= -2x+14}</font><BR>\n" );
document.write( "The curly braces are important so Desmos knows where one inequality ends and another begins. The first inequality doesn't need curly braces.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Points inside the blue shaded region are solutions to the system of inequalities.<BR>\n" );
document.write( "The point (4,1) is one such example. It makes  x ≥ 0 and y ≥ 0 true; it also makes y ≤ x+2 and y ≤ -2x+14 true as well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Confirmation for y ≤ x+2<BR>\n" );
document.write( "y ≤ x+2<BR>\n" );
document.write( "1 ≤ 4+2<BR>\n" );
document.write( "1 ≤ 6<BR>\n" );
document.write( "which is true\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Confirmation for y ≤ -2x+14<BR>\n" );
document.write( "y ≤ -2x+14<BR>\n" );
document.write( "1 ≤ -2(4)+14<BR>\n" );
document.write( "1 ≤ 6<BR>\n" );
document.write( "which is also true<BR>\n" );
document.write( "Therefore, the point (4,1) has been confirmed to work for the last two inequalities given. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'll let you try other points in the blue region.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Points on the boundary directly adjacent to the interior region are solutions as well<BR>\n" );
document.write( "However, we cannot include boundary points that aren't next to the blue interior. <BR>\n" );
document.write( "Eg: (2,4) is a solution but (-1,1) is not a solution even though it resides on a boundary line<BR>\n" );
document.write( "The point (-1,1) doesn't work because it doesn't satisfy x ≥ 0<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );