We are given a system of two linear equations: $4x - 2y = 4$ $-36x + 18y = -36$ We need to determine if the system has a unique solution, infinitely many solutions, or no solution, and state a reason.

1. Problem Description

We are given a system of two linear equations:

$4x - 2y = 4$

$-36x + 18y = -36$

We need to determine if the system has a unique solution, infinitely many solutions, or no solution, and state a reason.

2. Solution Steps

First, we simplify the given equations.

Equation (1): $4x - 2y = 4$. Divide by 2:

$2x - y = 2$

$y = 2x - 2$

Equation (2): $-36x + 18y = -36$. Divide by -18:

$2x - y = 2$

$y = 2x - 2$

Since both equations simplify to the same equation, $y = 2x - 2$, the system has infinitely many solutions. The graphs of the two equations represent the same line.

3. Final Answer

B. There are infinitely many solutions.

The graphs of the two equations represent the same line.