Question

when using the substitution method, how do you recognize an inconsistent system?

Answer 1

You'll get a nonsense statement like \(0 = 1\)

For example:
\[x + y = 3\]\[x+y = 4\]
From the first equation, \(y = 3-x\)
substitute into second equation
\[x+y=4\]\[x+(3-x) = 4\]\[3=4\]