document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79727>Question 79727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solving systems using substitution\r<BR>\n" );
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document.write( "x = y + 4<BR>\n" );
document.write( "y = x + 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57205 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=57205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = y + 4<BR>\n" );
document.write( "y = x + 4<BR>\n" );
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document.write( "This set of equations has no common solution. Let's try substitution.  The top equation<BR>\n" );
document.write( "is solved for x.  Therefore, you can take the right side of this equation and substitute<BR>\n" );
document.write( "it for x in the bottom equation.  If you do that the bottom equation becomes:<BR>\n" );
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document.write( "y = (y + 4) + 4<BR>\n" );
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document.write( "The parentheses are just there to show you where the substitution was made.  They are<BR>\n" );
document.write( "preceded by an implied + sign so you can just erase them to get:<BR>\n" );
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document.write( "y = y + 4 + 4<BR>\n" );
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document.write( "Do the addition on the right side:<BR>\n" );
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document.write( "y = y + 8<BR>\n" );
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document.write( "Just looking at this equation you should see that the right side can't equal the left side,<BR>\n" );
document.write( "but you can really see it if you subtract y from both sides.  If you do that you get:<BR>\n" );
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document.write( "0 = 8<BR>\n" );
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document.write( "Can't be.<BR>\n" );
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document.write( "What you can do to see the problem is to return to the original equation set and solve the<BR>\n" );
document.write( "top equation for y.  You can do that by subtracting 4 from both sides to get:<BR>\n" );
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document.write( "x - 4 = y <BR>\n" );
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document.write( "which can be transposed to:<BR>\n" );
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document.write( "y = x - 4<BR>\n" );
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document.write( "So now your equation set is:<BR>\n" );
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document.write( "y = x - 4 and<BR>\n" );
document.write( "y = x + 4<BR>\n" );
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document.write( "Both of these equations are in the slope intercept form.  In each of the equations<BR>\n" );
document.write( "the slope (which is the multiplier of the x term) is +1.  That means the slope is the <BR>\n" );
document.write( "same for both graphs.  The constant term on the right side of each equation is the point<BR>\n" );
document.write( "where the graph crosses the y-axis.  The graph of the first equation crosses the y-axis<BR>\n" );
document.write( "at - 4, and the graph of the second equation crosses the y-axis at +4.  Because these<BR>\n" );
document.write( "two graphs have the same slope they are separate lines, but they are parallel.  That <BR>\n" );
document.write( "means they never cross. But for linear equations such as these, for there to be a common<BR>\n" );
document.write( "solution, the lines need to cross, and the common solution is the point at which the lines<BR>\n" );
document.write( "intersect.  <BR>\n" );
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document.write( "Hope this helps you to understand why there is no common solution for this set of equations. </SPAN>\n" );
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