Question

It is known that if a+b=10 then a+b-c=10-c write the euclids axiom

Answer 1

The Euclid's Axiom to be applied here is 

"If equals be subtracted from equals, the remainders are equal"

It is because here equal a+b = 10 are subtracted from c = c which is equal.
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Answer 2

Here z has been added to two quantities that are equal.

So, by Euclid's second axiom, which states that, If equals are added to equals then wholes are equal,

⇒x+y+z=10+z

Hence, x+y+z=10+z is true by the second axiom of Euclid.