A linear system of equations is consistent if each of the equations have a common solution. So, we attempt to find a common solution that satisfies each equation in the following linear system:

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You can use substitution, linear combination, Gaussian elimination or whichever is your preferred method for solving a linear system of equations.

Eventually, you will either get some solution {x,y,z} that satisfies the system of equations, or you will observe some ridiculous contradiction (i.e., 2=8) which is your cue that you have inconsistent equations of a linear system. Be sure to check your work. Holla back if you are still stuck.

-Andy