Question

1. \

$$\begin{cases} -7x + 7y = -14 \\\\ -14x + 14y = -28 \\end{cases}$$

Explanation:

Step1: Simplify first equation

Divide by -7:
$$\frac{-7x}{-7} + \frac{7y}{-7} = \frac{-14}{-7}$$
$$x - y = 2$$

Step2: Simplify second equation

Divide by -14:
$$\frac{-14x}{-14} + \frac{14y}{-14} = \frac{-28}{-14}$$
$$x - y = 2$$

Step3: Analyze the system

Both equations simplify to the same linear equation, meaning they represent the same line. All points on the line $x - y = 2$ (or $y = x - 2$) are solutions.

Answer:

The system has infinitely many solutions, all pairs $(x, y)$ where $y = x - 2$ (or $x = y + 2$ for any real number $x$ or $y$).