For spaces X and Y , find their intersection X⋂Y and hence show that X⋂Y is a 1-dimensional subspace of R 4.

Question

Let $$X=\{(t,2t−s,s,3s−t) \mid s,t \in R\},$$ $$Y=\{(2q−p,p−q,3p−q,5q) \mid p,q \in R\}$$ with both $X$ and $Y$ subspaces of $\mathbb{R}^4$. Write down a basis for space $X$ and a basis for space $Y$. Hence, or otherwise, find a basis for $X + Y$.