SOLUTION: x+y=5 y+z=7 z+x=6 by matrix method

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Question 1120943: x+y=5
y+z=7
z+x=6
by matrix method
Found 3 solutions by josgarithmetic, Alan3354, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
(2,3,4)
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Solved by looking at it for 3 seconds.
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.
This system of equations is VERY SPECIAL, and there is VERY SPECIAL trick 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.



Answer.  The solution to the system is  (x,y,z) = (2,3,4).


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For closely related/similar problems see the lesson
    - The tricks to solve some word problems with three and more unknowns using mental math
in this site.


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