It is an inconsistent system of equations.
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Or perhaps you want examples?
One pair of inconsistent equations:
x + y = 4
x + y = 1
Another pair:
y = x2 + 3
y = 1
(In the first equation of this pair, y is minimised when x = 0, when its value is 3. But the second equation claims that y = 1.)
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the solution to a system is where the two lines intersect upon a graph.
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
Without a second independent equation, it's not a 'system' yet.
The solution to a system is an ordered pair (x,y) where the two lines intersect.
Without a second independent equation, it's not a 'system' yet.