document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=590619>Question 590619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write each equation in slope-intercept form. Then determine, without solving the system, whether the system has exactly one solution, no solution, or an infinite number of solutions   4x-3y=2                   5x+3y=6<BR>\n" );
document.write( "                              12x-9y=6                  10x+6y=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #375228 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=375228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x-3y=2                   <BR>\n" );
document.write( "5x+3y=6                   <BR>\n" );
document.write( "12x-9y=6                  <BR>\n" );
document.write( "10x+6y=2\r<BR>\n" );
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document.write( "y = (4/3)x - 2/3<BR>\n" );
document.write( "y = (-5/3)x + 2<BR>\n" );
document.write( "y = (4/3)x - 2/3<BR>\n" );
document.write( "y = -5/3)x + 1/3\r<BR>\n" );
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document.write( "2 of the lines have the same slope and the same y intercept so they are identical.  if you graph these equations, they will look like one line rather than 2.<BR>\n" );
document.write( "2 of the lines have the same slope and different y intercept so they are parallel.<BR>\n" );
document.write( "you have 1 set of identical lines and 1 set of parallel lines that will intersect in 2 separate points on a graph.<BR>\n" );
document.write( "for there to be a common solution, all 4 lines would have had to intersect in one common point on the graph.<BR>\n" );
document.write( "since there is not one common solution for all 4 equations, this system of equations has no solution.\r<BR>\n" );
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document.write( "a graph of the lines will show the 2 points of intersection.<BR>\n" );
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document.write( " </SPAN>\n" );
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