Solve this system of equations \( \left\{\begin{array}{l}3 x-3 y=15 \\ 4 x-3 y=18\end{array}\right. \) One solution: No solution Onfinite number of solutions

To solve the system of equations, we can start by rearranging both equations: 1. From the first equation \(3x - 3y = 15\), we can divide everything by 3 which simplifies to \(x - y = 5\) or \(x = y + 5\). 2. Now, substitute \(x\) from the first equation into the second equation \(4x - 3y = 18\): Substitute: \(4(y + 5) - 3y = 18\) Simplifying gives \(4y + 20 - 3y = 18\) which then simplifies to \(y + 20 = 18\). Thus, \(y = -2\). Plugging \(y\) back into \(x = y + 5\) gives us \(x = -2 + 5 = 3\). The solution to the system is \(x = 3\), \(y = -2\). Since we found a specific solution, the answer is: One solution.