Question

1. \

$$\begin{cases}2x - y = 4 \\\\ 1 = y - 2x + 5\\end{cases}$$

Explanation:

Step1: Simplify the second equation

First, we simplify the second equation \(1 = y - 2x + 5\). Let's rearrange it to the form of \(ax + by = c\).
Subtract \(y\) and add \(2x\) to both sides: \(2x - y + 1 = 5\), then \(2x - y = 5 - 1 = 4\). So the second equation simplifies to \(2x - y = 4\), which is the same as the first equation \(2x - y = 4\).

Step2: Analyze the system of equations

Now we have a system of linear equations:
\[

$$\begin{cases} 2x - y = 4 \\ 2x - y = 4 \end{cases}$$

\]
This means the two equations represent the same line. So there are infinitely many solutions, and the solutions are all the points \((x,y)\) that satisfy \(2x - y = 4\), which can be expressed as \(y = 2x - 4\) where \(x\) is any real number.

Answer:

The system of equations has infinitely many solutions, and the solutions are given by \(y = 2x - 4\) (where \(x\) is any real number) or in the form \(\{(x, 2x - 4) | x \in \mathbb{R}\}\)