Question

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

Explanation:

Step1: Simplify first equation

Divide by 2:
$x - 3y = 6$

Step2: Simplify second equation

Divide by -5:
$x - 3y = 6$

Step3: Analyze the two equations

Both equations are identical, meaning they represent the same line. So there are infinitely many solutions, which can be expressed in terms of a free variable. Let $y = t$ (where $t$ is any real number), then solve for $x$:
$x = 3t + 6$

Answer:

The system has infinitely many solutions, given by $\boldsymbol{x = 3t + 6}$, $\boldsymbol{y = t}$ where $t$ is any real number.