Easy math question parallel vectors Cartesian plane

part of a math question that i cant figure out

Find the relationship between p and q if

the vector (pi+qj) -(5i+1j) is parallel to the vector (4i+3j) ----------------> could not write in column form

ANSWER 3p - 4q = 1

but i'm getting 3p - 4q = 11

please help me thank you

(pi+qj) -(5i+1j) is parallel to the vector (4i+3j)

(p-5)i + (q-1)j is parallel to the vector 4i+3j

For Two vectors P and Q which are parallel to each other,

P = kQ, where k is an integer

So, p-5 = 4k and q-1 = 3k [Comparing the coefficients]
=> p-5/4 = k and q-1/3 = k
Equalizing -->
p-5/4 = q-1/3
=> 3p-15 = 4q-4
=> 3p - 4q = 11, which is the required answer