document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197261>Question 1197261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the lines ax + by = c and dx + ey = f are parallel whenever ae − bd = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830459 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=830459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Slopes should be equal.<BR>\n" );
document.write( "That is, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb=-d%2Fe ALIGN=MIDDLE  ALT=\"-a%2Fb=-d%2Fe\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb=d%2Fe ALIGN=MIDDLE  ALT=\"a%2Fb=d%2Fe\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ae=bd ALIGN=MIDDLE  ALT=\"ae=bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ae-bd=bd-bd ALIGN=MIDDLE  ALT=\"ae-bd=bd-bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ae-bd=0 ALIGN=MIDDLE  ALT=\"ae-bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "YOU WERE GIVEN TWO equations all in variables only and also are given condition that the two linear equations are for PARALLEL LINES.  That means, their slopes must be equal.  Use the variable available in the two given equations.  Maybe one might start with the \"whenever\" condition and work backward, but I did this in the other direction.  IF the two lines parallel,.... then \"ae-bd=0\".\r<BR>\n" );
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document.write( "If you expected some graphing, then no do.  You were not given two specific linear equations; you were given two linear equations in general.  This is a symbolism exercise. </SPAN>\n" );
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