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 set of ordered pairs \( f = \{(1,1), (2,3), (0,1), (1,3)\} \), we will follow these steps:

### Step 1: Set Up the Equations
From the ordered pairs, we can create equations based on the function definition.

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