Ineed on answering my math homework question

So you need to solve for p and q, using solution addition/subtraction.

for this particular question I will subtract. p+q=4 from 4p+q=1

4p+q=1
-(p+q)=4

3p +0q = -3
3p=-3
3/3p=-3/3
p=-1

With the value of p found insert p into one of the original equations 
--> Usually choosing the easier one is easier

p+q=4    Inset p=-1
-1+q=4
q=4+1
q=5

Therefore,
q=5, p=-1