Vectors, how to calculate v and w when (v+w) and (v-w) are given

I know how to solve for (v + w) and (v -w) if v and w are given [I just add or subtract the individual components], but I can't seem to figure out how to approach the problem going backwards. Problem is:

If
(v + w) = (5, 1) and
(v - w) = (1, 5)

compute v and w.

Thank you. Will make sure to pick best answer.

v+w and v-w are vectors which can be added and subtracted just like any other vectors.

(v + w) = (5, 1)
(v - w) = (1, 5)

add the two vectors
2v = (6, 6)
v = (3,3)

subtract the two vectors
2w = (4, -4)
w = (2, -2)

You can use some vector algebra here. Since V + W = (5,1) and V - W = (1,5), then 2V = (6, 6). You get this by adding the two given equations together to eliminate the W. And we simplify to get V = (3,3). We can substitute this vector in for V in either equation to find our other vector W. (3,3) + W = (5,1) will give us W = (2,-2).

(v + w) + (v - w) = 2v
<5, 1> + <1, 5> = 2v
<5 + 1, 1 + 5> = 2v
<6, 6> = 2v
v = <6/2, 6/2> = <3, 3>

v + w = <5, 1>
w = <5, 1> - <3, 3>
= <5 - 3, 1 - 3>
w = <2, -2>

add the two equations and we get 2v=(6,6) => v=(3,3)
thus w=(2,-2)