System of equations

x -2y + 3z = 0 ......[1]
2x+ 5y + 6z = 0...... [2]

[1] * 2 :
2x -4y + 6z = 0 ...... [3]

[2] - [3] :
9y = 0
y = 0

Put y = 0 into [1] :
x - 0 + 3z = 0
x = -3z
x/z = -3


Hence, y = 0 and x : z = -3 : 1

(To solve for 3 unknowns, there must be at least 3 equation.)
(There are only 2 equations, and thus the exact solutions of x an z cannot befound.)

Actually x : z = -3 : 1 can be further expressed to give x = -3t and z = t : t∈R