document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184906>Question 1184906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x+3y+2z=16<BR>\n" );
document.write( "Find the value of x,y and z. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815567 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=815567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sum of the pieces must be equal to 16.<BR>\n" );
document.write( "the solution needs to be unique is what i think you are looking for.\r<BR>\n" );
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document.write( "we'll work with y first and then worry about x and z.\r<BR>\n" );
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document.write( "the equation is 2x + 3y + 2z = 16\r<BR>\n" );
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document.write( "3y can either be 3 or 6 or 9 or 12 or 15.\r<BR>\n" );
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document.write( "3y = 3 or 9 are no good because 16 - 3 = 13 and 16 - 9 = 7, neither or which are divisible by 2.\r<BR>\n" );
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document.write( "3y = 15 is no good because you only have 1 left for 2x and 2z which is not enough, and it is not divisible by 2 anyway.\r<BR>\n" );
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document.write( "your options are therefore 3y = 6 or 3y = 11\r<BR>\n" );
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document.write( "if 3y = 6, then you get 2x + 6 + 2z = 16<BR>\n" );
document.write( "subtract 6 from both sides of the equation to get:<BR>\n" );
document.write( "2x + 2z = 10<BR>\n" );
document.write( "your possible values are:<BR>\n" );
document.write( "2x = 2, 2z = 8<BR>\n" );
document.write( "2x = 4, 2z = 6<BR>\n" );
document.write( "2x = 6, 2z = 4<BR>\n" );
document.write( "2x = 8, 2z = 2\r<BR>\n" );
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document.write( "these are all possibilities, but there is not one unique solution.\r<BR>\n" );
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document.write( "if 3y = 12, then you get 2x + 12 + 2z = 16<BR>\n" );
document.write( "subtract 12 from both sides of the equation to get:<BR>\n" );
document.write( "2x + 2z = 4<BR>\n" );
document.write( "2x can be equal to 2<BR>\n" );
document.write( "2z can be equal to 2\r<BR>\n" );
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document.write( "this, of course, assumes that none of 2x or 3y or 2z can be equal to 0.\r<BR>\n" );
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document.write( "you get a unique solution when x = 1 and y = 4 and z = 1<BR>\n" );
document.write( "you then get:<BR>\n" );
document.write( "2x + 3y + 2z = 2 + 12 + 2 = 16.\r<BR>\n" );
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document.write( "i would go with that.\r<BR>\n" );
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document.write( "x = 1<BR>\n" );
document.write( "y = 4<BR>\n" );
document.write( "z = 1\r<BR>\n" );
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document.write( "2x + 3y + 2z = 2 + 12 + 2 = 16\r<BR>\n" );
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document.write( " </SPAN>\n" );
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