document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105374>Question 1105374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that 2x + 3y - 6 = 0 & 4x  +6y = 0 are parallel </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720191 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with:\r<BR>\n" );
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document.write( "2x + 3y - 6 = 0<BR>\n" );
document.write( "4x + 6y = 0\r<BR>\n" );
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document.write( "add 6 to both sides of the first eqution and leave the second equation as is to get:\r<BR>\n" );
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document.write( "2x + 3y = 6<BR>\n" );
document.write( "4x + 6y = 0\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 2 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "4x + 6y = 12<BR>\n" );
document.write( "4x + 6y = 0\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "0 = 12.\r<BR>\n" );
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document.write( "all the variable disappeared and the equation is untrue, so there is no solution which means the lines never intersect which means the lines are parallel.\r<BR>\n" );
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document.write( "alternatively, convert both equations to slope intercept form to get:\r<BR>\n" );
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document.write( "4x + 6y = 12 becomes 6y = -4x + 12 which becomes y = -4/6 * x + 2.<BR>\n" );
document.write( "4x + 6y = 0 becomes 6y = -4x + 0 which becomes y = -4/6 * x.\r<BR>\n" );
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document.write( "the equations have the same slope and a different y-intercept which means they are parallel.\r<BR>\n" );
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document.write( "from the following graph, you can see that both forms of each equation are identical because they draw the same line.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/122401.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( "these two lines will always be 2 vertical units from each other, no matter what the value of x is.\r<BR>\n" );
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document.write( "this can be seen on the graph at x = -6, x = 0, and x = 6.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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