How to know if a linear system has no solution


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How do you determine whether a system of linear equations has no solutions, one solution, or infinitely many solutions?

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The answer to this is

If the lines are the same, the equations are dependent linear equations. Using the graph of y = x and x + 2y = 6, shown below, determine how many solutions the system has. Then classify the system as consistent or inconsistent and the equations as dependent or independent. The lines intersect at one point.


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