Let `f = {(1,1), (2, 3), (0, 1), (1, 3)}`be a function from `Z to Z` defined by `f(x) = a x + b`, for some integers `a, b.`
Determine `a, b`.

Explanation

To determine the values of \( a \) and \( b \) in the function \( f(x) = ax + b \) given the ordered pairs \( f = \{(1, 1), (2, 3), (0, 1), (1, 3)\} \), we can follow these steps:

### Step 1: Set up equations using the given pairs
From the ordered pairs, we can set up equations based on the function definition \( f(x) = ax + b \).

1. From the pair \( (1, 1) \):
\[
f(1) = a(1) + b = 1 \implies a + b = 1 \quad \text{(Equation 1)}
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