# Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y, and z cannot contain an equation in the form $y=mx+b$.

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rogreenhoxa8

The general form of a system in three variables x,y,z has equation in the general form:
$akx+bky+ckz=dk$
If one of the coefficients ck of the variables z is zero, we can isolate y and bring that equation to the form $y=mx+b.$
$akx+bky=dk$
$bky=-akx+dk$
$y=-\left(ak/bk\right)x+dk/bk$