I'm trying to complete the following exercise:

Let V be the set of vectors $({x}_{1},{x}_{2},{x}_{3},{x}_{4})\in {\mathbb{R}}^{4}$ such that

$2{x}_{1}-3{x}_{2}-{x}_{3}+{x}_{4}=0$

${x}_{1}-{x}_{2}+2{x}_{3}-{x}_{4}=0$

Show that V is a subspace of ${\mathbb{R}}^{4}$ and find a basis for V.

I already showed that V is a subspace of ${\mathbb{R}}^{4}$, but I'm having trouble finding a basis for V. Any help is welcome

Let V be the set of vectors $({x}_{1},{x}_{2},{x}_{3},{x}_{4})\in {\mathbb{R}}^{4}$ such that

$2{x}_{1}-3{x}_{2}-{x}_{3}+{x}_{4}=0$

${x}_{1}-{x}_{2}+2{x}_{3}-{x}_{4}=0$

Show that V is a subspace of ${\mathbb{R}}^{4}$ and find a basis for V.

I already showed that V is a subspace of ${\mathbb{R}}^{4}$, but I'm having trouble finding a basis for V. Any help is welcome