Question 149241
3p-4q=4

First, solve for p:
add 4q to each side:
3p=4+4q  divide each side by 3

p=(4+4q)/3 
By inspection, we see that q must be less than 7, otherwise p will be greater than 10.  Lets assign values for q between 0 and 6 and see what we get for p:

q=0; p=4/3------------------no good --not a single-digit number
q=1; p=5/3-------------------no good---not a single-digit number
q=2; p=4---------------------BINGO!!!!!
q=3; p=16/3-------------------no good---not a single-digit number
q=4; p=20/3---------------------no good---not a single-digit number
q=5; p=8------------------------BINGO!!!!!!!!!!!!
q=6; p=28/3---------------------no good---not a single-diogit number

Answer:
q=2; p=4
and
q=5; p=8


Hope this helps---ptaylor