Algebra: system of equations

Question

Assume the system of equations:

a+b=p²

b+c=q²

a+c=r²

I don't really see how one get

a=(p²+r²-q²)/2

Answer 1

subtract the second equation from the first and you get:

a - c = p2 - q2

add that equation to the 3rd equation and you get

2a = p2 - q2 + r2

divide both sides by 2 and you get

a = (p2 - q2 + r2)/2

rearrange terms and you get

a = (p2 + r2 - q2)/2

Answer 2

Subtracts equation 1 MINUS equation 2:

A-c= p^2-q^2

Then adds that to the 3rd equation:

A-c= p^2-q^2

A+c= r^2. +

2a=p^2-q^2+r^2

One obtains The final result and completes the proof by dividing both sides by 2 and rearranging the numerator via commutative property