Question 263280
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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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        There is a way much shorter and much more elegant to solve the problem

        than the method used by @mananth.


        See my solution below.



<pre>
Your starting equations are

    3x +  y = 17, 
    5y +  z = 14 ,
    3x + 5z = 41.


Add all three equations.  You will get

    6x + 6y + 6z = 17 + 14 + 41,

or

    6(x + y + z) = 72.


Divide both sides by 6

    x + y + z = 72/6 = 12.


At this point, the problem is just solved completely.


<U>ANSWER</U>.  x + y + z = 12.
</pre>

Solved in the shortest way.


I am 129% sure that the true meaning and the destination of this problem 
is to teach you to solve it by this short and elegant method.