Table of Variables

You almost have found a simple solution: try x[i] instead of x[[i]]

Solve[{x[1] + x[2] == 2, x[1] - x[2] == 1}, {x[1], x[2]}]

{{x[1] -> 3/2, x[2] -> 1/2}}

List of this variables:

Array[x,2]

{x[1], x[2]}

Use Symbol to convert a string into a symbol...

Table[Symbol["$x" <> ToString@i], {i, 5}]

{$x1, $x2, $x3, $x4, $x5}

One word of caution. I tend to keep programmatically generated variables prepended with a $ to avoid any collisions with any other variables I might've defined. Just from experience.