document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246064>Question 246064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each system by the addition method. Determine whether<BR>\n" );
document.write( "the equations are independent, dependent, or inconsistent\r<BR>\n" );
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document.write( "x-y= 3<BR>\n" );
document.write( "-6x+6y=17 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179717 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=179717\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equations are:\r<BR>\n" );
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document.write( "x-y = 3<BR>\n" );
document.write( "-6x+6y = 17\r<BR>\n" );
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document.write( "multiply first equation by 6 to get:\r<BR>\n" );
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document.write( "6x-6y = 18\r<BR>\n" );
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document.write( "add to second equation to get:\r<BR>\n" );
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document.write( "6x-6y = 18<BR>\n" );
document.write( "plus<BR>\n" );
document.write( "-6x+6y = 17<BR>\n" );
document.write( "equals<BR>\n" );
document.write( "0 + 0 = 35\r<BR>\n" );
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document.write( "this becomes 0 = 35 which is false.\r<BR>\n" );
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document.write( "there is no common solution to this system of equations.\r<BR>\n" );
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document.write( "Here's a <a  rel=nofollow HREF= \"http://www.jcoffman.com/Algebra2/ch3_1.htm\" target = \"_blank\">definition<a/> of independent, dependent, or inconsistent.\r<BR>\n" );
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document.write( "If you have 1 valid solution then the equations are independent.\r<BR>\n" );
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document.write( "If you have multiple valid solutions, then the equations are dependent.\r<BR>\n" );
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document.write( "If you have 0 valid solutions then the solution are inconsistent.\r<BR>\n" );
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document.write( "These equations are inconsistent.\r<BR>\n" );
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document.write( "If we graphed this solution, we would find the lines are parallel.\r<BR>\n" );
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document.write( "Another way is to convert the equations to slope-intercept form and see if the slopes are the same.\r<BR>\n" );
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document.write( "If they are, the lines are parallel.\r<BR>\n" );
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document.write( "Your first equation is x-y = 3\r<BR>\n" );
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document.write( "Convert to slope-intercept form and you get y = x-3 meaning the slope is 1.\r<BR>\n" );
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document.write( "Your second equation is -6x + 6y = 17\r<BR>\n" );
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document.write( "Convert to slope-intercept form and you get y = x + 17/6 meaning the slope is 1.\r<BR>\n" );
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document.write( "The slopes are the same so the lines are parallel meaning they will never intercept meaning the solution is inconsistent.\r<BR>\n" );
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document.write( "A graph of these two equations is shown below:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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