document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106663>Question 1106663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which expression can be substituted for x in the top equation of the following system  to solve the system by substitution?  What is the solution?\r<BR>\n" );
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document.write( "&#8722;2x&#8722;3y=&#8722;13<BR>\n" );
document.write( "x+y=6\r<BR>\n" );
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document.write( "The choices are :\r<BR>\n" );
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document.write( "1) &#8722;y+6,&#8201;(5,1)\r<BR>\n" );
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document.write( "2) y+6, (-1/5 ,1/5)       that's meaning 1 over neg 5,and 1 over 5<BR>\n" );
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document.write( "3)-3/2y+13/2 (5,1)\r<BR>\n" );
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document.write( "4) 6&#8722;y,&#8201;(1,5)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721701 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=721701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equations to solve are:\r<BR>\n" );
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document.write( "&#8722;2x &#8722; 3y = &#8722;13\r<BR>\n" );
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document.write( "x + y = 6 \r<BR>\n" );
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document.write( "in the second equation, solve for x to get x = -y + 6.\r<BR>\n" );
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document.write( "in the first equation, replace x with (-y + 6) to get -2(-y+6) -3y = -13.\r<BR>\n" );
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document.write( "simplify to get 2y - 12 - 3y = -13\r<BR>\n" );
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document.write( "combine like terms to get -y - 12 = -13\r<BR>\n" );
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document.write( "solve for y to get y = 1.\r<BR>\n" );
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document.write( "go back to your original equations.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "&#8722;2x &#8722; 3y = &#8722;13\r<BR>\n" );
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document.write( "x + y = 6 \r<BR>\n" );
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document.write( "replace y in the second equation with 1 to get x + 1 = 6\r<BR>\n" );
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document.write( "solve for x to get x = 5.\r<BR>\n" );
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document.write( "your solution is x = 5 and y = 1.\r<BR>\n" );
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document.write( "replace x with 5 and y with 1 in the first original equation to get &#8722;2(5) &#8722; 3(1) = &#8722;13\r<BR>\n" );
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document.write( "simplify to get -10 - 3 = -13 which reduces to -13 = -13 which is true.\r<BR>\n" );
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document.write( "this conforms the solution is correct.\r<BR>\n" );
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document.write( "your solution is (x,y) = (5,1).\r<BR>\n" );
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document.write( "your choices are:\r<BR>\n" );
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document.write( "1) &#8722;y+6,&#8201;(5,1) <BR>\n" );
document.write( "2) y+6, (-1/5 ,1/5) that's meaning 1 over neg 5,and 1 over 5\r<BR>\n" );
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document.write( "3)-3/2y+13/2 (5,1) <BR>\n" );
document.write( "4) 6&#8722;y,&#8201;(1,5) \r<BR>\n" );
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document.write( "eliminate selection 2 and 4 because their coordinate solution is not (5,1).\r<BR>\n" );
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document.write( "that leaves selection 1 or selection 3.\r<BR>\n" );
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document.write( "you were asked to substitute for x in the first equation.\r<BR>\n" );
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document.write( "you did that by solving for x in the second equation and then substituting for x in the first equation.\r<BR>\n" );
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document.write( "when you solved for x in the second equation, you got x = -y + 6.\r<BR>\n" );
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document.write( "you solution is therefore selection 1.\r<BR>\n" );
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document.write( "selection 1 is:\r<BR>\n" );
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document.write( "1) &#8722;y+6,&#8201;(5,1) \r<BR>\n" );
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document.write( "the first part of that selection is the value that you substituted for x.\r<BR>\n" );
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document.write( "the second part of that selection is the solution in coordinate form.\r<BR>\n" );
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