Question

1. \

$$\begin{cases} x - 3y = 7 \\\\ 2x - 6y = 12 \\end{cases}$$

Explanation:

Step1: Analyze the system of equations

We have the system \(

$$\begin{cases}x - 3y=7\\2x - 6y = 12\end{cases}$$

\). Notice that the second equation \(2x-6y = 12\) can be simplified by dividing both sides by 2. We get \(x - 3y=6\).

Step2: Compare with the first equation

The first equation is \(x - 3y = 7\). Now we have two equations: \(x-3y = 7\) and \(x - 3y=6\). But a linear expression \(x - 3y\) cannot be equal to two different values (\(7\) and \(6\)) at the same time. So, this system of linear equations has no solution.

Answer:

The system of equations \(

$$\begin{cases}x - 3y = 7\\2x - 6y=12\end{cases}$$

\) has no solution.