No. Here is a simple example where this is not the case:
x + y = 0
x + y = 1
If you subtract the first equation from the second, you get 0 = 1, which is clearly impossible. Graphically, you get two parallel lines, which never cross.
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A system of linear equations that has at least one solution is called consistent.
You don't need ANY factor. To find a unique solution, or a few, you would usually need to have as many equations as you have variables.
At least two - otherwise you have just one equation, not a system.
You have two unknown variables, x and y. You therefore need at least two independent equations to find a solution.
It means that at least one of the equations can be expressed as a linear combination of some of the other equations. A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations. For example, if you have x + 2y = 3 and 2x + y = 4 Then adding 2 times the first and 3 times the second gives 8x + 7y = 18 This is, therefore, dependent on the other 2. If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.