Solution: (1) inequality set 2x+y? 4≤0x+y？ 3≤0x≥0y≥0 indicates the plane area as follows:

(2) When the straight line k=x+3y passes through the point (0,0), the minimum value of k is 0.

When the straight line k=x+3y passes through point A (0,3), the maximum value of k is 9.

So the range of k=x+3y is: [0,9].

(3) The area s =12× (3+2 )×1+12×1= 72.

The area falling within the area of X ∈ [1, 2] is 1.

Therefore, the probability that the point (x, y) falls within the region of x ∈ [1, 2] is p = 172 = 27.