Question

how to determine whether the pairs of equations intersect, parallel or coincide

Answer 1

if a1/a2 is not equal to b1/b2 then the lines are intersecting

if a1/a2 is equal to b1/b2 but not equal to c1/c2 then the lines are parallel

if a1/a2 is equal to b1/b2 also equal to c1/c2 then the lines are co-incident

*given that a1 and a2 are the coefficients of x
                  b1 and b2 are the coefficients of y
                &c1 and c2 are constants