Solve the Linear Equation: 3x - y = -5 and 9x - 3y = -15 for Consistency

To solve this system of equations, we need to determine the relationship between the two equations. The given equations are:

$3x - y = -5$

$9x - 3y = -15$

Let's examine the second equation:

Notice that if we multiply the first equation by 3, we obtain:

$3(3x - y) = 3(-5)$

which simplifies to:

$9x - 3y = -15$

This is exactly the same as the second given equation. Thus, the second equation is a multiple of the first equation, indicating that they represent the same line in the coordinate plane.

When two equations represent the same line, any point on this line will satisfy both equations. Therefore, there are infinitely many solutions to this system. That is, there are infinitely many points $(x, y)$ that can satisfy both equations.

Therefore, the solution to the problem is Infinite solutions.