Final answer:
A consistent linear system with six equations and three variables does not guarantee a unique solution; it often has infinitely many solutions. Solving requires identifying the knowns and unknowns, and using substitution or elimination to find solutions, double-checking algebraic steps for accuracy.
Step-by-step explanation:
If a linear system has six equations and three variables and is consistent, we cannot guarantee that the solution is unique. Instead, we can often expect that there will be infinitely many solutions. This is because having more equations than variables typically indicates that some of the equations are redundant or that the equations describe the same line or plane in three-dimensional space. To solve the system, we would look for a set of equations that can be combined to eliminate variables and narrow down the solution set. We must ensure that our manipulations of these equations remain true to the original system to avoid introducing errors or contradictions.
When examining a linear system, we identify the knowns, which are the constants in the equations, while the variables we need to solve for are the unknowns. The goal is to solve for these unknowns by finding equations, or a set of equations, that make it possible to isolate each variable and find its value. If the system is consistent and there are more equations than unknowns, we typically utilize substitution and elimination techniques, while always rechecking our algebraic steps. Consistency alone cannot guarantee a unique solution, as the system might depict the same relationship in multiple ways, leading to a situation with infinitely many solutions.