Please help me understand this problem.

Let a, b, and c be any real numbers and let x = (X1, X2 ..., Xi, ..., Xn) be a data set with a sample mean x and Let y = ()1, y2 ..., yi, ..., )n) be a data set with a sample mean y. Let z = ax + by + c such that z = (ax, + by1 + c, ax2 + by2 + c ..., ax; + by; + c, ..., axn + byn+ c). Zn Z2 Zi Z1 Show that z = ax + by + c