SOLUTION: Find all values of p and q such that 3p+7q=1 and 5p=14q+53

Question 1035769: Find all values of p and q such that 3p+7q=1 and 5p=14q+53
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
From the system
3p+7q=1
5p=14q+53
we can solve by doubling the first one, solving for 14q and plugging that into the second one, like this...
6p + 14q = 2
14q = -6p + 2
5p = (-6p + 2) + 53
5p = -6p + 55
11p = 55
p = 5
Now plug that in to the top one and get
3(5) + 7q = 1
15 + 7q = 1
7q = -14
q = -2
(5, -2) is your solution.
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