document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102927>Question 102927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following systems of linear inequalities graphically\r<BR>\n" );
document.write( "\n" );
document.write( "3x-y<=6<BR>\n" );
document.write( "x>=1<BR>\n" );
document.write( "y<=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74848 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=74848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-y%3C=6 ALIGN=MIDDLE  ALT=\"3x-y%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Draw the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+-+y+=+6 ALIGN=MIDDLE  ALT=\"3x+-+y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x+-6 ALIGN=MIDDLE  ALT=\"y+=+3x+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then shade the area between x-axis and line to the left starting in the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+x+%2B+-1+y+=+6 ALIGN=MIDDLE  ALT=\"3+x+%2B+-1+y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+-3%2F-1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-3%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 6/3 = 2.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/-1 = -6.</LI><LI>Slope is -3/-1 = 3.</LI><LI> Equation in slope-intercept form: y=3*x+-6.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+-6-8%2C+-6%2B8%2C+3%2Ax%2B-6+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+-6-8%2C+-6%2B8%2C+3%2Ax%2B-6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
document.write( "</TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=1 ALIGN=MIDDLE  ALT=\"x%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is a line parallel to y-axis; shade everything to the right starting from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>this equation defines a vertical line. <BR>\n" );
document.write( "  <UL><BR>\n" );
document.write( "    <LI> X intercept: 1. X intercept is the intersection of the line with the x axis. </LI><BR>\n" );
document.write( "    <LI> Y intercept: not defined (the line IS vertical)</LI><BR>\n" );
document.write( "    <LI> Slope: not defined, can be thought of as infinite</LI><BR>\n" );
document.write( "  </UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+1-5%2C+1%2B5%2C+-10%2C+10%2C+1000000x-1000000%2A1+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+1-5%2C+1%2B5%2C+-10%2C+10%2C+1000000x-1000000%2A1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
document.write( "</TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=3 ALIGN=MIDDLE  ALT=\"y%3C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >this is a line parallel to x-axis; shade everything up starting from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3 ALIGN=MIDDLE  ALT=\"y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>This equation defines a horizontal line. There is no X intercept. Y intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F1=3 ALIGN=MIDDLE  ALT=\"3%2F1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+3+-+10%2C+3%2B10%2C+3%2F1+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+3+-+10%2C+3%2B10%2C+3%2F1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );