So what i did was set x1...xk as the basis of W1 intersect W2. Then I said i could extend this basis for w1 and w2, so B1= x1...xk,y1..ym and B2 = x1... xk, z1... zn. I take the union of the two and claim that it is a basis for B1+B2. the generating part is trivial, but i cant seem to prove linear independence. Ive tried contradiction, but that gives me that z1 is a linear combination of xs ys and zs, which doesnt look like much of a contradiction.