Solve the System of Equations: 3x - y = -10 and 9x - 3y = -15

To solve this problem, let's apply the elimination method:

• Step 1: Write down the given equations: $3x - y = -10$ and $9x - 3y = -15$.
• Step 2: Observe that the second equation is 3 times the first equation. Multiply the first equation by 3 for alignment: $3(3x - y) = 3(-10)$ becomes $9x - 3y = -30$.
• Step 3: Compare the two resulting equations: $9x - 3y = -30$ and $9x - 3y = -15$.
• Step 4: Notice these equations suggest a contradiction as the left-hand side is the same ($9x - 3y$), but the right-hand sides are different ($-30$ vs. $-15$).

As the comparison shows a contradiction, these lines are parallel and do not intersect.
Therefore, the system of equations has no solution.