Question

7、\

$$\begin{cases}2x - 6y = 12\\\\-5x + 15y = -30\\end{cases}$$

Explanation:

Step1: Simplify the first equation

Divide the first equation \(2x - 6y = 12\) by 2: \(x - 3y = 6\), so \(x = 3y + 6\).

Step2: Substitute into the second equation

Substitute \(x = 3y + 6\) into \(-5x + 15y = -30\):
\(-5(3y + 6) + 15y = -30\)
Expand: \(-15y - 30 + 15y = -30\)
Simplify: \(-30 = -30\).
This is an identity, meaning the system has infinitely many solutions (the two lines are coincident). The general solution is \(x = 3y + 6\) (or \(y\) can be any real number, and \(x\) is determined by \(y\)).

Answer:

The system has infinitely many solutions, with the general solution \(x = 3y + 6\) (where \(y\) is any real number)