Question 1120943
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This system of equations is <U>VERY SPECIAL</U>, and there is <U>VERY SPECIAL trick</U> to solve it.


x + y = 5      (1)
y + z = 7      (2)
z + x = 6      (3)


Add equations (1), (2) and (3)  (both sides). You will get


2x + 2y + 2z = 5 + 7 + 6 = 18,    or, equivalently,


x + y + z = 9.     (4)


Now  subtract equation (1) from equation (4). You will get  z = 9-5 = 4.


Next subtract equation (2) from equation (4). You will get  x = 9-7 = 2.


Finally, subtract equation (3) from equation (4). You will get  y = 9-6 = 3.



<U>Answer</U>.  The solution to the system is  (x,y,z) = (2,3,4).
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For closely related/similar problems see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/The-trick-to-solve-some-word-problems-with-three-and-more-unknowns.lesson>The tricks to solve some word problems with three and more unknowns using mental math</A>

in this site.