Final answer:
The linear system has one solution.
Step-by-step explanation:
The given equation is 5x - 1 - 15x - 3y = 3. To determine the number of solutions, we need to simplify and rearrange the equation. Group like terms together: 5x - 15x - 1 - 3y = 3. Combine the x terms: -10x - 1 - 3y = 3. Rearrange the equation: -10x - 3y = 3 + 1. Simplify: -10x - 3y = 4.
The equation -10x - 3y = 4 is a linear equation in standard form. A linear equation can have one solution, no solution, or an infinite number of solutions. To determine the number of solutions, we need to check the slopes of the equation. If the slopes are equal, then the system has an infinite number of solutions. If the slopes are not equal, then the system has one solution.
In this case, the equation -10x - 3y = 4 is in the form y = mx + b, where m is the slope. The slope of this equation is -10/3. Since the slope is not zero, the system has one solution.