Question: In ECC Cryptography, how to add points ALGEBRAICALLY? For example y ^ 2 = x ^ 3 + x + 6 over Z 1 1

In ECC Cryptography, how to add points ALGEBRAICALLY?
For example y^2= x^3+ x +6 over Z11,
a)(10,9)+(3,5)=(10,2), why?
b)3(7,2)=(8,3), why?
Please just explain how ECC math works BUT NOT GRAPHICALLY. I want to do by hand.

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