ax + by = c, where a, b, c are in arithmetic sequence .......(1)

dx + ey = f, where d, e, f are in arithmetic sequence .......(2)

a, b, c are in arithmetic sequence

or

now on substituting values of b & e in (1) and (2), we get

solve (3) and (4) to get x=-1 and y=2.

for nature of solutions:- for unique solution

ratio of coefficient of x isn't equal to \ratio of coefficient of x

therefore system of linear eq have unique solution x=-1 and y=2.