document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045300>Question 1045300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show graphically that -(a-b)=-a+b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660711 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=660711\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = a and y = b.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "-(x - y) = -x + y\r<BR>\n" );
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document.write( "simplify to get -x + y = -x + y\r<BR>\n" );
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document.write( "add x to both sides of the equation and subtract y from both sides of this equation to get:\r<BR>\n" );
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document.write( "-x + x + y - y = -x + x + y - y, which results in:\r<BR>\n" );
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document.write( "0 = 0\r<BR>\n" );
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document.write( "since all the variables disappeared from the equation and the equation is true, this means that any values of x and y will satisfy the original equation.\r<BR>\n" );
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document.write( "in other words, the equation is an identity.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "let x = 15 and y = 20 (numbers off the top of my head).\r<BR>\n" );
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document.write( "-(x - y) = -x + y becomes:\r<BR>\n" );
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document.write( "-(15 - 20) = -15 + 20\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "-15 + 20 = -15 + 20\r<BR>\n" );
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document.write( "it's plain to see that this equation is true.\r<BR>\n" );
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document.write( "if you add 15 to both sides of this equation and subtract 20 from both sides of this equation, you will get:\r<BR>\n" );
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document.write( "0 = 0\r<BR>\n" );
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document.write( "now to graphing this equation.\r<BR>\n" );
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document.write( "what i find is that it doesn't graph on a 2 dimensional plane.\r<BR>\n" );
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document.write( "it does graph on a 3 dimensional planes and the result is that z = 0.\r<BR>\n" );
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document.write( "on a 2 dimensional plane, you start out with:\r<BR>\n" );
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document.write( "-(x-y) = -x + y\r<BR>\n" );
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document.write( "to graph this, you solve for y.\r<BR>\n" );
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document.write( "start with -(x-y) = -x + y\r<BR>\n" );
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document.write( "simplify to get -x + y = -x + y\r<BR>\n" );
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document.write( "add x to both sides of this equation and subtract y from both sides of this equation to get:\r<BR>\n" );
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document.write( "0 = 0.\r<BR>\n" );
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document.write( "there's nothing to graph.\r<BR>\n" );
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document.write( "on a 3 dimensional plane, you get:\r<BR>\n" );
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document.write( "z1 = -(x - y)\r<BR>\n" );
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document.write( "z2 = -x + y\r<BR>\n" );
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document.write( "set z = z1 - z2.\r<BR>\n" );
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document.write( "this becomes z = -(x - y) - (-x + y) which becomes z = -x  + y + x - y which becomes z = 0.\r<BR>\n" );
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document.write( "the 3 dimensional graph is a plane at z = 0.\r<BR>\n" );
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document.write( "this means that any value of x and y will make z = 0.\r<BR>\n" );
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document.write( "the 2 dimensional graph will show nothing.\r<BR>\n" );
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document.write( "the 3 dimensional graph will show z = 0.\r<BR>\n" );
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document.write( "here's what the 3 dimensional graph will look like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/082701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the plane is empty which means that any value of x and y will satisfy the equation.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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