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To solve the system of equations, we can add the two equations together to eliminate the variable "b".
(a+b) + (a-b) = 10 + 2
2a = 12
a = 6
Substituting the value of "a" back into one of the original equations:
a + b = 10
6 + b = 10
b = 4
Therefore, the solution to the system of equations is a = 6 and b = 4.