document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198986>Question 1198986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the solution to the system of inequalities given below:\r<BR>\n" );
document.write( "\n" );
document.write( "x≤2<BR>\n" );
document.write( " <BR>\n" );
document.write( "y>−2x+2<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 #832695 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52794)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Graph the solution to the system of inequalities given below:<BR>\n" );
document.write( "x ≤ 2<BR>\n" );
document.write( "y > −2x+2<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The plot in the post by @Theo is &nbsp;INCORRECT.\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to bring you a correct solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "They want you solve this system of two inequalities \r\n" );
document.write( "\r\n" );
document.write( "   x <= 2          (1)\r\n" );
document.write( "\r\n" );
document.write( "   y > -2x+2       (2)\r\n" );
document.write( "\r\n" );
document.write( "by graphing.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, plot two straight lines in a coordinate plane \r\n" );
document.write( "\r\n" );
document.write( "    x = 2           (1')\r\n" );
document.write( "\r\n" );
document.write( "    y = -2x+2       (2')\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28330%2C+330%2C+-5%2C+5%2C+-10%2C+10%2C%0D%0A%0D%0A+++++++graph%28+330%2C+330%2C+-5%2C+5%2C+-10%2C+10%2C%0D%0A++++++++++200%2A%28x-2%29%2C+-2x%2B2%29%2C%0D%0A+++++++locate%28-2%2C+++8%2C+++the%29%2C%0D%0A+++++++locate%28-1%2C+6.5%2C+solution%29%2C%0D%0A+++++++locate%280.5%2C++5%2C+++set%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "      Plot x = 2 (red)  and  y = -2x+2 (green)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that the line x = 2 (red) is vertical line, parallel to y-axis.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The solution set to the given inequalities are the points of the coordinate plane, \r\n" );
document.write( "\r\n" );
document.write( "    that are, at the same time,  on the left of the red line  <U>AND</U>  above the green line.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "These points are inside one of the four angles, formed by the two lines, where you see the words \"the solution set\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The points of the red   line above the intersection point are included to the solution set. \r\n" );
document.write( "\r\n" );
document.write( "The points of the green line are  NOT INCLUDED  to the solution set.\r\n" );
document.write( "\r\n" );
document.write( "The intersection point  DOES NOT BELONG  to the solution set.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "On solving inequalities in two variables graphically, &nbsp;look into the lesson\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Graphs/Solving-systems-of-inequalities-in-two-unknown-graphically-in-a-coordinate-plane.lesson>Solving systems of inequalities in two unknown graphically in a coordinate plane</A> \r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Learn the method from there.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Happy learning (!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );