Final answer:
To determine if a system has one unique solution without solving it, count the number of equations and unknowns and check if they are equal.
Step-by-step explanation:
In order to determine if a system has one unique solution without actually solving the equations, you need to look at the number of equations and the number of unknowns in the system. If the number of equations is equal to the number of unknowns, and the equations are not dependent on each other, then the system has one unique solution.
For example, if you have the following system of equations:
x + y = 3
2x - y = 1
There are two equations and two unknowns (x and y). The equations are not dependent on each other, so this system has one unique solution.