Algebra: find all the solutions of each system of equations?

X^1 - 2X^2 + X^3 = 1

X^2 - 2X^3 + X^4 = 0

X^3 - 2X^4 + X^5 = 2

X^4 - 2X^5 + X^6 = 0

X^5 - 2X^6 + X^7 = 1

im not sure how to start such a big system of equations ....do you have to isolate all the different x's(x^1,x^2....)?

any help much appreciated!!!!