document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949663>Question 949663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please solve this algebra: 2-x+y=3-y+x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579792 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=579792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "start with 2-x+y = 3-y+x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add y to both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2-x+2y = 3+x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add x to both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2+2y = 3+2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 2 from both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2y = 1+2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 2 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 1/2 + x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "rearrange the terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = x + 1/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your original equation of 2 - x + y = 3 - y + x is true when y = x + 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let x = 2 and y = 2.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 - x + y becomes 2 - 2 + 2.5 which becomes 2.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3 - 2.5 + 2 becomes 5 - 2.5 which becomes 2.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your original equation of 2-x+y = 3-y+x is true when y = x + 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "just to confirm some more, use another value of x and y that satisfy the equation of y = x + 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let x = 15 and y = 15.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 - x + y becomes 2 - 15 + 15.5 which becomes -13 + 15.5 which becomes 2.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3 - y + x becomes 3 - 15.5 + 15 which becomes 18 - 15.5 which becomes 2.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it doesn't matter what the value of x and y are as long as y = x + 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when y = x + 1/2, the value of the expression on the left side of the equation and on the right side of the equation will always be equal to 2.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the answer to your question is that the original equation will always be true when y = x + 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the reason why each side of the equation will always be equal to 2.5 is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with 2 - x + y = 3 - y + x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let y = x + 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 - x + (x + 1/2) = 3 - (x + 1/2) + x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 - x + x + 1/2 = 3 - x - 1/2 + x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 + 1/2 = 3 - 1/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms again to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 and 1/2 = 2 and 1/2 which is the same as 2.5 = 2.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when you asked to solve this, i presume you asked to solve for y in terms of x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that answer is that y = x + 1/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "as long as y = x + 1/2, the original equation will be true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the fact that each side of the equation will always be equal to 2.5 when you replace y with x + 1/2 is additional information that i don't believe you needed to know, although you might find it interesting.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "at least i did. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );