Substitution of 2 for y in either of the original equations yields x = -1.
Therefore, it is true that {(-1 , 2 )} is the Solution set of all pairs of linear equations where the coefficients and right-hand member of each separate equation are terms of an arithmetic sequence and the common difference, d, in both arithmetic sequences is the same, ( d ≠ 0 ). Thus it has been shown that Nicolai demonstrated a special case of the general situation. In his special case n is the fourth term of an arithmetic sequence having a as the first term.