Introduction:
In electrical engineering, the terms "linear" and "time-invariant" are used to describe the behavior of systems. A linear system satisfies the properties of additivity and homogeneity, while a time-invariant system maintains its behavior over time.

Explanation:
To determine the linearity and time-invariance of the given system, let's analyze its properties.

1. Linearity:
A system is linear if it satisfies two properties: additivity and homogeneity.

- Additivity: If x1(t) produces y1(t) and x2(t) produces y2(t), then for any constant α and β, the system should satisfy αx1(t) + βx2(t) → αy1(t) + βy2(t).

In the given system, y(t) = max(0, x(t)). Let's consider two inputs x1(t) and x2(t) that produce outputs y1(t) and y2(t) respectively.

- For x1(t), the output y1(t) = max(0, x1(t)).
- For x2(t), the output y2(t) = max(0, x2(t)).

Now, let's consider αx1(t) + βx2(t) as the input to the system.

- αx1(t) + βx2(t) = α(max(0, x1(t))) + β(max(0, x2(t))).

To check additivity, we compare the output of the system for the input αx1(t) + βx2(t) with αy1(t) + βy2(t).

- Output for αx1(t) + βx2(t) = max(0, α(max(0, x1(t))) + β(max(0, x2(t))).
- αy1(t) + βy2(t) = α(max(0, x1(t))) + β(max(0, x2(t))).

Since both outputs are equal, the system satisfies additivity.

- Homogeneity: If x(t) produces y(t), then for any constant α, the system should satisfy αx(t) → αy(t).

In the given system, let's consider x(t) as the input that produces y(t) as the output.

- For x(t), the output y(t) = max(0, x(t)).

To check homogeneity, we compare the output of the system for the input αx(t) with αy(t).

- Output for αx(t) = max(0, αx(t)).
- αy(t) = α(max(0, x(t))).

Since both outputs are equal, the system satisfies homogeneity.

Since the given system satisfies both additivity and homogeneity, it is linear.

2. Time-Invariance:
A system is time-invariant if its behavior remains the same over time.

In the given system, y(t) = max(0, x(t)). Let's consider an input x(t) that produces output y(t).

If we delay the input by a certain time τ, the new input becomes x(t - τ). The output for the delayed input should be y(t - τ).

- For x(t - τ), the output y(t - τ) = max(0, x(t - τ)).

Comparing the original output y