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A system is consistent if there is at least one solution.
for example x+y=1 and 3x+y-2
A system is inconsistent if it has no solutions
(When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as a proof that 0 = 1.)
for example 3x+7y=3 and 3x+7y=10
A system of equations are dependent if both the equations represent the same equation
for example 2x+3y=2 and 4x+6y=4