document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824664>Question 824664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of the line which passes through the point of intersection of 5x-3y+2=0 and x+3y+1=0 and is parallel to 2x+3y+3=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496644 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=496644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the intersection:<BR>\n" );
document.write( "Add the equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+-+3y+%2B+2+=+0+ ALIGN=MIDDLE  ALT=\"+5x+-+3y+%2B+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+3y+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+x+%2B+3y+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x+%2B3+=+0+ ALIGN=MIDDLE  ALT=\"+6x+%2B3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x+=+3+ ALIGN=MIDDLE  ALT=\"+6x+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+3y+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+x+%2B+3y+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+%2B+3y+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+1%2F2+%2B+3y+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+-3%2F2+ ALIGN=MIDDLE  ALT=\"+3y+=+-3%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-1%2F2+ ALIGN=MIDDLE  ALT=\"+y+=+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The intersection is (1/2, -1/2 )<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Now find the slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+3y+%2B+3+=+0+ ALIGN=MIDDLE  ALT=\"+2x+%2B+3y+%2B+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+-2x+-+3+ ALIGN=MIDDLE  ALT=\"+3y+=+-2x+-+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-%282%2F3%29%2Ax+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+-%282%2F3%29%2Ax+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+-2%2F3+ ALIGN=MIDDLE  ALT=\"+m+=+-2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "I can write the general point-slope equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+-+%28-1%2F2%29+%29+%2F+%28+x+-+1%2F2+%29+=+-2%2F3+ ALIGN=MIDDLE  ALT=\"+%28+y+-+%28-1%2F2%29+%29+%2F+%28+x+-+1%2F2+%29+=+-2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%2B+1%2F2+=+-2%2F3%2A%28+x+-+1%2F2+%29+ ALIGN=MIDDLE  ALT=\"+y+%2B+1%2F2+=+-2%2F3%2A%28+x+-+1%2F2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%2B+1%2F2+=+%28-2%2F3%29%2Ax+%2B+1%2F3+ ALIGN=MIDDLE  ALT=\"+y+%2B+1%2F2+=+%28-2%2F3%29%2Ax+%2B+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+ ALIGN=MIDDLE  ALT=\"+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y+%2B+3+=+-4x+%2B+2+ ALIGN=MIDDLE  ALT=\"+6y+%2B+3+=+-4x+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6y+=+-4x+-1+ ALIGN=MIDDLE  ALT=\"+6y+=+-4x+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-2%2F3%29%2Ax+-+1%2F6+ ALIGN=MIDDLE  ALT=\"+y+=+%28-2%2F3%29%2Ax+-+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "does it go through (1/2, -1/2) ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-2%2F3%29%2Ax+-+1%2F6+ ALIGN=MIDDLE  ALT=\"+y+=+%28-2%2F3%29%2Ax+-+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2F2+=+%28-2%2F3%29%2A%281%2F2%29+-+1%2F6+ ALIGN=MIDDLE  ALT=\"+-1%2F2+=+%28-2%2F3%29%2A%281%2F2%29+-+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2F2+=+-1%2F3+-+1%2F6+ ALIGN=MIDDLE  ALT=\"+-1%2F2+=+-1%2F3+-+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3%2F6+=+-2%2F6+-+1%2F6+ ALIGN=MIDDLE  ALT=\"+-3%2F6+=+-2%2F6+-+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3%2F6+=+-3%2F6+ ALIGN=MIDDLE  ALT=\"+-3%2F6+=+-3%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );