The equation of plane 3y- 1=0 does not contain x and z, y= 1/3, and none of its points are on the xOz plane.

That is, this plane is parallel to the coordinate plane xOz.

Plane y+z=0, and the equation does not contain X.

The normal vector of the plane is (0, 1, 1), and the direction vector of the x axis is (1, 0).

These two vectors are perpendicular, that is, the X axis is either parallel to the plane or on the plane.

The origin (0,0,0) is on the plane and also on the X axis.

So the straight line where the X axis is located is on the plane.