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"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.