Question

1. \

$$\begin{cases} -2x + 6y = -4 \\\\ 4x - 12y = 8 \\end{cases}$$

Explanation:

Step1: Simplify first equation

Divide the first equation $-2x + 6y = -4$ by $-2$:
$$x - 3y = 2$$

Step2: Simplify second equation

Divide the second equation $4x - 12y = 8$ by $4$:
$$x - 3y = 2$$

Step3: Analyze the two equations

Both simplified equations are identical, meaning they represent the same line.

Answer:

The system has infinitely many solutions, which can be expressed as $x = 3y + 2$ where $y$ is any real number, or all points $(3y+2, y)$ for $y \in \mathbb{R}$.