In equation 3x – y ≥ 3 and 4x – 4y > 4

The correct option is: "Have solution for positive x and y".

To understand why this is correct, let us analyze the given system of linear inequalities:
1) $3x-y\ge 3$
2) $4x-4y>4$

Let us simplify the second inequality first by dividing all terms by 4:
$x-y>1$
Which can be rewritten as:
$y<x-1$

Now, let us rewrite the first inequality in terms of $y$:
$3x-3\ge y$
Which is:
$y\le 3x-3$

For a solution to exist for positive values of $x$ and $y$ (i.e., $x>0$ and $y>0$), we can choose a specific test point that satisfies all conditions.
Let us test the point $(x,y)=(3,1)$, where both $x$ and $y$ are positive:
For the first inequality:
$3\left(3\right)-1=9-1=8\ge 3$ (This is true).
For the second inequality:
$4\left(3\right)-4\left(1\right)=12-4=8>4$ (This is also true).

Since there exists at least one point in the first quadrant where both $x>0$ and $y>0$ that satisfies both inequalities, the system has a solution for positive $x$ and $y$.