For this system

x + y = 2    (1)
y + z = 4    (2)
z + x = 9    (3)


there is SPECIAL method of solution.

First, add all three equations (1), (2) and (3).  You will get


2x + 2y + 2z = 15,     or, equivalently,

x + y + z = 7.5.    (4)


Now subtract eq(1) from eq(4). You will get

z = 7.5 - 2 = 5.5.    The unknown "z" is just found.


Next subtract eq(2) from eq(4). You will get

x = 7.5 - 4 = 3.5.    The unknown "x" is just found.



Finally, subtract eq(3) from eq(4). You will get

y = 7.5 - 9 = -1.5.    The unknown "y" is just found.


Answer.  x= 3.5;  y= -1.5;  z= 3.5.