The problem asks to solve the system of equations: $4x - 9y = 4$ $-20x + 45y = -20$ and to determine if there is a unique solution, infinitely many solutions, or no solution. We also need to select the statement that best explains the solution.

1. Problem Description

The problem asks to solve the system of equations:

$4x - 9y = 4$

$-20x + 45y = -20$

and to determine if there is a unique solution, infinitely many solutions, or no solution. We also need to select the statement that best explains the solution.

2. Solution Steps

First, we can try to eliminate one of the variables. Multiply the first equation by 5:

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

$20x - 45y = 20$

Now we have the following system of equations:

$20x - 45y = 20$

$-20x + 45y = -20$

Add the two equations together:

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

$0 = 0$

Since we obtained the identity $0 = 0$, this indicates that the two equations are linearly dependent, which means they represent the same line. Therefore, there are infinitely many solutions.

Also, since the equations are the same, the graphs of the two equations represent the same line.

3. Final Answer

There are infinitely many solutions.

The graphs of the two equations represent the same line.