document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158543>Question 158543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by graphing.<BR>\n" );
document.write( "3x-2y=4<BR>\n" );
document.write( "-6x+4y=7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116804 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=116804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solving the equation by algebraic means, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax-2%2Ay%29=4 ALIGN=MIDDLE  ALT=\"%283%2Ax-2%2Ay%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%2Ax%2B4%2Ay%29=7 ALIGN=MIDDLE  ALT=\"%28-6%2Ax%2B4%2Ay%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solving for y in the first equation, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%283%2Ax%29%2F2%29-2%29 ALIGN=MIDDLE  ALT=\"y=%28%283%2Ax%29%2F2%29-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting this for y in the second equation, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-6%2Ax%2B4%29%2B4%2A%283%2Ax%2F2+-+2%29+=+7 ALIGN=MIDDLE  ALT=\"y=%28-6%2Ax%2B4%29%2B4%2A%283%2Ax%2F2+-+2%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6%2Ax+%2B+6%2Ax+-+8+=+7 ALIGN=MIDDLE  ALT=\"y=-6%2Ax+%2B+6%2Ax+-+8+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since the x cancels out we are left with<BR>\n" );
document.write( "-8=7<BR>\n" );
document.write( "which means there is no solution.<BR>\n" );
document.write( "looking at both equations in y = slope intercept form, we see<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2Ax%2F2%29-2 ALIGN=MIDDLE  ALT=\"y=%283%2Ax%2F2%29-2\"   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=y=%286%2Ax%2F4%29%2B%287%2F4%29 ALIGN=MIDDLE  ALT=\"y=%286%2Ax%2F4%29%2B%287%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "general form of the slope intercept form of the equation is y=m*x+b<BR>\n" );
document.write( "where m is the slope and b is the y intercept when x = 0.<BR>\n" );
document.write( "slope of the first equation is 3/2<BR>\n" );
document.write( "slope of the second equation is 6/4 which simplifies to 3/2.<BR>\n" );
document.write( "slopes are equal so lines are parallel.<BR>\n" );
document.write( "solving by equation below shows that right away.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-15%2C15%2C%283x-4%29%2F2%2C%286x%2B7%29%2F4%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-15%2C15%2C%283x-4%29%2F2%2C%286x%2B7%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );