I've just been handed a project for my Linear Algebra course, so far I can't even begin to grasp the concept of affine subsets. Anyway I was wondering if anyone could help with the first question in which I am meant to illustrate the concept:

Show that:

M = {x=(x1,...x4) exists inR^4 : x1 - 2*x2 + x3 = 3 and x1 + 5*x3 - 2*x4=1}

is an affine subset ofR^4.

Sorry about the notation here. x1 means x subscript 1.

If anyone can help I would be really grateful.