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How do you solve system of equations and tell if they're consistant and independant,consistant and dependent,and inconsistant?

If you find no solutions then the system is inconsistent.

Suppose you have N variables and M equations (N larger than or equal to M). Then, if you obtain a N-M dimensional solution space, i.e. the solution contains N-M undetermined parameters, the M equations are independent and consistent.

If the dimension of the solution space is larger, then the set of equations is dependent.

Also, if M is larger than N and there are solutions then the equations are dependent.

Thanks for the help but that made no sense to me. This is the problem I have:Choose the correct description of the system of equations. x+2y=7 and 3x-2y=5. I tried to solve it and I got (7,8) and I have to tell if its consistant etc.

If you add the equations you get:

4 x = 12 -->

x = 3

If you insert x = 3 in the first equation you get

2 y = 4 --->

y = 2

We found a solution, so the system of equations is consistent. We have two variables and two equations. N = 2, M= 2 and thus N - M = 0. The solution has no free parameters if the equations are independent. That's the case here.

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