Is the set a subspace??

Question

Is the set, S = {x in R³: 2x + 3y - 4z = 0 OR 4x - 2y + 3z = 0}

a subspace of R³ ? Show your working.

Thank You

Answer 1

Both 2x + 3y - 4z = 0 and 4x - 2y + 3z = 0 are equations of planes through the origin, so both are subspaces of R^3.