document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071539>Question 1071539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of k so that these lines are coincident.\r<BR>\n" );
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document.write( "R:y = 2x + 1\r<BR>\n" );
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document.write( "S:x = -6t + k <BR>\n" );
document.write( "  y = 4t + 2\r<BR>\n" );
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document.write( "Line S is an equation system </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686555 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=686555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> line R is y = 2x + 1<BR>\n" );
document.write( "line S is x = -6t + k<BR>\n" );
document.write( "you are also given that y = 4t + 2\r<BR>\n" );
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document.write( "line R becomes 4t + 2 = 2x + 1<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = (4t + 1)/2\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = -6t + k and x is equal to (4t + 1)/2\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "(4t + 1)/2 = -6t + k\r<BR>\n" );
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document.write( "multiply both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "4t + 1 = -12t + 2k\r<BR>\n" );
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document.write( "add 12t to both sides of this equation to get:\r<BR>\n" );
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document.write( "4t + 1 + 12t = 2k\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "16t + 1 = 2k\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 and solve for k to get:\r<BR>\n" );
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document.write( "k = 8t + 1/2\r<BR>\n" );
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document.write( "when k = 8t + 1/2, your original equations become:\r<BR>\n" );
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document.write( "y = 2x + 1<BR>\n" );
document.write( "x = -6t + k<BR>\n" );
document.write( "y = 4t + 2<BR>\n" );
document.write( "k = 8t + 1/2\r<BR>\n" );
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document.write( "since y = 2x + 1 and y = 4t + 2, then you get:\r<BR>\n" );
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document.write( "2x + 1 = 4t + 2\r<BR>\n" );
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document.write( "since x = -6t + k and k = 8t + 1/2, you get:\r<BR>\n" );
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document.write( "x = -6t + 8t + 1/2\r<BR>\n" );
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document.write( "2x + 1 = 4t + 2 becomes:\r<BR>\n" );
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document.write( "2 * (-6t + 8t + 1/2) + 1 = 4t + 2\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "2 * (2t + 1/2) + 1 = 4t + 2\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "4t + 1 + 1 = 4t + 2\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "4t + 2 = 4t + 2\r<BR>\n" );
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document.write( "the lines are coincident when their equations are the same.\r<BR>\n" );
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document.write( "this occurs when k = 8t + 1/2.\r<BR>\n" );
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document.write( "this is all based on what i think you are asking because i'm not totally sure that i understood exactly what your problem is asking.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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