General definition of System of Linear Equations says that
"If The system has a unique solution, It has independent set of Equations"
Consider the system of linear equations $$x-2y=-1$$ $$3x+5y=8$$ $$4x+3y=7$$ As we can see from the below graph that all the 3 line intersect at a single point $\implies$ System has a unique solution. But at the same time system is not independent as any equation can be derived from the algebraic manipulations of other two equations. So, how definition is true.
Above System of equations are an example of
Overdetermined SystemA system of equations is considered overdetermined, If there are more equations than unknowns. The only cases where the overdetermined system will have a solution is when it contains enough linearly dependent equations that the number of independent equations does not exceed the number of unknowns [Wiki].