# 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.

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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avortarF
We have to study if a system of linear equations in three variables x,y,z can contain an equation in the form y=mx+b
$Ax+By+Cz=D$

The equations of a linear system with 3 variables are of the form:
$A=m$
$B=-1$
$C=0$
$D=-n$
A,B,C,D can have the values:
$mx-y=-n$
In this particular case, the equation is written:
$mx-y+y+n=-n+y+n$
$y=mx+n$
We add y+n on both sides and we have:
Thus it is possible to have equations in the form $y=mx+n$ in a linear system with 3 variables which means the statement doesnt make sense.