STATEMENT - 1 : If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is consistent.
STATEMENT - 2 : If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is inconsistent.
Consistency means the equation gives the solution which is when lines intersect, but when lines are parallel they don’t intersect. Hence no solution is obtained.