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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.

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1 Answer

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Above System of equations are an example of Overdetermined System

A 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].

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