document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90077>Question 90077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by substitution. Please help.<BR>\n" );
document.write( "8x-4y = 16<BR>\n" );
document.write( "y = 2x -4<BR>\n" );
document.write( "Thanks in advance.<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 #65861 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=65861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the two equations:<BR>\n" );
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document.write( "8x-4y = 16<BR>\n" );
document.write( "y = 2x -4<BR>\n" );
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document.write( "The problem is to solve them by substitution.<BR>\n" );
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document.write( "Note that the second equation already tells us the value for y. It says that y is equal<BR>\n" );
document.write( "to 2x - 4.<BR>\n" );
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document.write( "Therefore, we can go to the first equation and substitute 2x - 4 for y. When you do that<BR>\n" );
document.write( "the first equation is transformed to:<BR>\n" );
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document.write( "8x - 4(2x - 4) = 16<BR>\n" );
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document.write( "Multiply out the left side by multiplying -4 times each of the terms in the parentheses to<BR>\n" );
document.write( "get:<BR>\n" );
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document.write( "8x - 8x + 16 = 16<BR>\n" );
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document.write( "Ooops. We know that something is wrong because the 8x and - 8x cancel each other and the<BR>\n" );
document.write( "equation is reduced to 16 = 16.<BR>\n" );
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document.write( "We need to go back to the original set of equations and see what the problem might be.<BR>\n" );
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document.write( "The original set of equations is:<BR>\n" );
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document.write( "8x-4y = 16<BR>\n" );
document.write( "y = 2x -4<BR>\n" );
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document.write( "Let's multiply the second equation (both sides, all terms) by -4. When you do that the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "-4y = -8x + 16<BR>\n" );
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document.write( "Next let's get it into the form of the first equation by adding 8x to both sides. <BR>\n" );
document.write( "When you do that the second equation becomes:<BR>\n" );
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document.write( "8x - 4y = 16<BR>\n" );
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document.write( "This means that the second equation is identical to the first equation. Therefore, every<BR>\n" );
document.write( "solution to the first equation is also a solution to the second equation also. And if you<BR>\n" );
document.write( "graphed both equations, the graphs would lie on top of each other. The equations have no<BR>\n" );
document.write( "singular solution ... every solution to one is a solution to the other also.<BR>\n" );
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document.write( "Hope this helps to explain the difficulty you encountered in solving this set of equations.<BR>\n" );
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