We are given a system of two linear equations: $4x - 9y = 4$ $-20x + 45y = -20$ We need to determine if the system has a unique solution, infinitely many solutions, or no solution. If there is a unique solution, we need to find it.

1. Problem Description

We are given a system of two linear equations:

$4x - 9y = 4$

$-20x + 45y = -20$

We need to determine if the system has a unique solution, infinitely many solutions, or no solution. If there is a unique solution, we need to find it.

2. Solution Steps

We can use the method of elimination to solve the system. Let's multiply the first equation by 5:

$5(4x - 9y) = 5(4)$

$20x - 45y = 20$

Now, we have two equations:

$20x - 45y = 20$

$-20x + 45y = -20$

Let's add the two equations:

$(20x - 45y) + (-20x + 45y) = 20 + (-20)$

$0 = 0$

Since we obtained the identity $0=0$, this indicates that the two equations are dependent, and there are infinitely many solutions.

3. Final Answer

B. There are infinitely many solutions.