document.write( "Question 263280: Given the equations 3x + y = 17, 5y + z = 14 and 3x + 5z = 41, what is the value of the sum x + y + z? \n" ); document.write( "

Algebra.Com's Answer #853996 by ikleyn(53727) $\"\"$ $\"About$

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\n" ); document.write( "Given the equations 3x + y = 17, 5y + z = 14 and 3x + 5z = 41, what is the value of the sum x + y + z?
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\n" ); document.write( "\n" ); document.write( "        There is a way much shorter and much more elegant to solve the problem\r
\n" ); document.write( "\n" ); document.write( "        than the method used by @mananth.\r
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\n" ); document.write( "\n" ); document.write( "        See my solution below.\r
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document.write( "Your starting equations are\r\n" );
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document.write( "    3x +  y = 17, \r\n" );
document.write( "    5y +  z = 14 ,\r\n" );
document.write( "    3x + 5z = 41.\r\n" );
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document.write( "Add all three equations.  You will get\r\n" );
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document.write( "    6x + 6y + 6z = 17 + 14 + 41,\r\n" );
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document.write( "or\r\n" );
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document.write( "    6(x + y + z) = 72.\r\n" );
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document.write( "Divide both sides by 6\r\n" );
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document.write( "    x + y + z = 72/6 = 12.\r\n" );
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document.write( "At this point, the problem is just solved completely.\r\n" );
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document.write( "ANSWER.  x + y + z = 12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in the shortest way.\r
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\n" ); document.write( "\n" ); document.write( "I am 129% sure that the true meaning and the destination of this problem
\n" ); document.write( "is to teach you to solve it by this short and elegant method.\r
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