document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891960>Question 891960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of x,y and z which make all these equations true:<BR>\n" );
document.write( "Y+z=78 , z+x= 70 and x+y=54 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #540180 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=540180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have:\r<BR>\n" );
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document.write( "y + z = 78 (equation 1)<BR>\n" );
document.write( "x + z = 70 (equation 2)<BR>\n" );
document.write( "x + y = 54 (equation 3)\r<BR>\n" );
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document.write( "start with equation 1.<BR>\n" );
document.write( "solve for y to get y = 78 - z\r<BR>\n" );
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document.write( "start with equation 2.<BR>\n" );
document.write( "solve for x to get x = 70 - z\r<BR>\n" );
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document.write( "start with equation 3.<BR>\n" );
document.write( "replace x with 70 - z<BR>\n" );
document.write( "replace y with 78 - z<BR>\n" );
document.write( "equation becomes 70 - z + 78 - z = 54<BR>\n" );
document.write( "combine like terms to get 148 - 2z = 54<BR>\n" );
document.write( "add 2z to both sides of the equation and subtract 54 from both sides of the equation to get 94 = 2z<BR>\n" );
document.write( "solve for z to get z = 47\r<BR>\n" );
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document.write( "start with equation 2 to get:\r<BR>\n" );
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document.write( "x + z = 70<BR>\n" );
document.write( "replace z with 47<BR>\n" );
document.write( "equation becomes x + 47 = 70<BR>\n" );
document.write( "subtract 47 from both sides of the equation to get x = 23\r<BR>\n" );
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document.write( "so far you have x = 23 and z = 47\r<BR>\n" );
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document.write( "start with equation 1 to get:\r<BR>\n" );
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document.write( "y + z = 78<BR>\n" );
document.write( "replace z with 47 to get y + 47 = 78<BR>\n" );
document.write( "subtract 47 from both sides of the equation to get y = 31\r<BR>\n" );
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document.write( "you now have x = 23, y = 31, z = 47<BR>\n" );
document.write( "those are your solutions.<BR>\n" );
document.write( "replace x,y,z in the original equations and they should hold true.\r<BR>\n" );
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document.write( "y + z becomes 31 + 47 = 78 which is true.<BR>\n" );
document.write( "x + z becomes 23 + 47 = 70 which is true.<BR>\n" );
document.write( "x + y becomes 23 + 31 = 54 which is true.\r<BR>\n" );
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document.write( "you did good.\r<BR>\n" );
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document.write( "another way to solve it is to treat it like 3 sets of equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "the 3 equations are:\r<BR>\n" );
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document.write( "y + z = 78 (equation 1)<BR>\n" );
document.write( "x + z = 70 (equation 2)<BR>\n" );
document.write( "x + y = 54 (equation 3)\r<BR>\n" );
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document.write( "take the first 2 equations and solve them simultaneously to remove z.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "y + z = 78<BR>\n" );
document.write( "x + z = 70\r<BR>\n" );
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document.write( "subtract second equation from first equation to get y - x = 8 (equation 4)\r<BR>\n" );
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document.write( "take that and solve it simultaneously with equation 3 to get:\r<BR>\n" );
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document.write( " x + y = 54 (equation 3)<BR>\n" );
document.write( "-x + y = 8 (equation 4)\r<BR>\n" );
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document.write( "add the 2 equations together to get 2y = 62<BR>\n" );
document.write( "solve for y to get y = 31\r<BR>\n" );
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document.write( "so far you have y = 31\r<BR>\n" );
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document.write( "go back to equation 1 to get:\r<BR>\n" );
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document.write( "y + z = 78 (equation 1)<BR>\n" );
document.write( "replace y with 31 to get:|<BR>\n" );
document.write( "31 + z = 78<BR>\n" );
document.write( "solve for z to get z = 47\r<BR>\n" );
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document.write( "so far you have y = 31 and z = 47\r<BR>\n" );
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document.write( "go back to equation 2 to get:\r<BR>\n" );
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document.write( "x + z = 70 (equation 2)<BR>\n" );
document.write( "replace z with 47 to get:<BR>\n" );
document.write( "x + 47 = 70<BR>\n" );
document.write( "solve for x to get x = 23\r<BR>\n" );
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document.write( "now you have x = 23, y = 31, z = 47\r<BR>\n" );
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document.write( "those are your solutions as before.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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