document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=679822>Question 679822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me graph the solutions of the system: y<2x-6 and 2x+3y<3 and find the point of intersection. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #422073 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><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=422073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Starting with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y%3C2x-6%29 ALIGN=MIDDLE  ALT=\"highlight%28y%3C2x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y intercept is -6<BR>\n" );
document.write( "Plot (0, -6)<BR>\n" );
document.write( "The x intercept is where y = 0<BR>\n" );
document.write( "0=2x-6<BR>\n" );
document.write( "6=2x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2 ALIGN=MIDDLE  ALT=\"6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=x<BR>\n" );
document.write( "Plot (3, 0)<BR>\n" );
document.write( "Draw a dashed line through the intercepts, so at to NOT include the points on the line.<BR>\n" );
document.write( "Lightly shade the area below the line, since y is <<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Using 2x+3y<3<BR>\n" );
document.write( "Isolate the y variable<BR>\n" );
document.write( "3y < -2x+3<BR>\n" );
document.write( "y < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2F3%29x++%2B+3%2F3 ALIGN=MIDDLE  ALT=\"%28-2%2F3%29x++%2B+3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y%3C%28-2%2F3%29x%2B1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y%3C%28-2%2F3%29x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y intercep is 1<BR>\n" );
document.write( "Plot (0,1)<BR>\n" );
document.write( "The x intercept is where y = 0<BR>\n" );
document.write( "0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2F3%29x%2B1 ALIGN=MIDDLE  ALT=\"%28-2%2F3%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 0)<BR>\n" );
document.write( "Draw a dashed line through these intercepts.  It is dashed so as to NOT include the points on the line.  Lightly shade the area below the line since y is <.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "To find the intersection, set the equations equal to each other.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-6+=+%28-2%2F3%29x+%2B+1 ALIGN=MIDDLE  ALT=\"2x-6+=+%28-2%2F3%29x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+%282%2F3%29x+=+1+%2B+6 ALIGN=MIDDLE  ALT=\"2x+%2B+%282%2F3%29x+=+1+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F3%29x+=+7 ALIGN=MIDDLE  ALT=\"%288%2F3%29x+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%283%2F8%29+=+21%2F8 ALIGN=MIDDLE  ALT=\"x+=+7%283%2F8%29+=+21%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute this x variable into either of the equations to solve for y<BR>\n" );
document.write( "y = 2<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F8 ALIGN=MIDDLE  ALT=\"21%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 6 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2821%2F4%29+-+6%284%2F4%29+=+-3%2F4 ALIGN=MIDDLE  ALT=\"%2821%2F4%29+-+6%284%2F4%29+=+-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The intersection point is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F8 ALIGN=MIDDLE  ALT=\"21%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "The area that is shaded for both inequalities is the solution<BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cy%3C2x-6%2Cy%3C%28-2%2F3%29x%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cy%3C2x-6%2Cy%3C%28-2%2F3%29x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".....................<BR>\n" );
document.write( "Delighted to help; feel free to email if you have further questions.<BR>\n" );
document.write( "HomeworkHelpers@readingboosters.com<BR>\n" );
document.write( "-Reading Boosters<BR>\n" );
document.write( "Website: www.MyHomeworkAnswers.com <BR>\n" );
document.write( "Wanting for others what we want for ourselves.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );