I have a simple question, that I believe I know the answer to, but want to know

Question

I have a simple question, that I believe I know the answer to, but want to know for sure and why:

Determine whether the equations form a linear system

x = 4
2x = 8

Please do not write just yes or no, please provide at least a simple sentence to explain why. Thanks! Will rate lifesaver!

Explanation / Answer

The answer, put simply, is no. This is because the equations are equivalent: 2x = 8 x = 4 --> 2(x) = 2(4) --> 2x = 8 Therefore they are not a system of equations, they are both simple, already-solved equations of the form x = c where c is a constant c = 4. In order for you to have a linear system, you need 'as many unknowns as you have equations,' and the equations cannot be equivalent. Therefore, having two equations for one unknown would simply result in one equation put in two different forms, which is what you have here.

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