Final answer:
The question deals with a linear system in Mathematics, focusing on finding values of a parameter for which the system has no solutions, infinite solutions, or a unique solution. Methods involve examining the gradients and intercepts of the equations involved.
Step-by-step explanation:
The provided information seems to discuss strategies for solving various problems, including linear equations and kinematics in Physics. However, the initial question seems to indicate a desire for help with a linear systems problem (a set of linear equations) in Mathematics. Specifically, the student is asking about conditions under which the system has no solutions, infinite solutions, and how to find a unique solution given a certain parameter 'a'.
For (a), a system of equations has no solutions when the lines are parallel but have different y-intercepts, which means the equations represent the same gradient but different intercepts. For (b), there are infinite solutions when the equations are identical, meaning they have the same gradient and y-intercept. For (c), a unique solution exists when the system consists of two intersecting lines, which means they have different gradients.
Without the exact equations, we cannot provide specific values for 'a'. However, the general approach would involve equating the coefficients of the terms of the equations if they are in the form of ax + by = c, where 'x' and 'y' are the variables, and 'a', 'b', and 'c' are coefficients. Varying 'a' will change the slope of the line and potentially alter the solution set of the system.