Final answer:
A system has a unique solution when the equations are linearly independent and match the number of variables. To find values of 'a' for a unique solution, one must use known values and solve for 'a' without additional unknowns.
Step-by-step explanation:
The student is asking about conditions for a unique solution in a system of equations. In mathematics, for a system of equations to have a unique solution, the equations must be linearly independent and the number of equations must be equal to the number of variables. When we list all known values and identify the unknowns, we look for an equation that contains only one unknown or a system where the number of distinct equations matches the number of unknowns.
To find the values of 'a' for which the system has a unique solution, we need to avoid equations with more than one unknown. In your cases, you should look at the final conditions and enter them into an equation that solves for the unknown value without introducing new variables. This way, you can solve for 'a' and ensure it results in a unique solution.