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.