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Question # 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.

Forms of linear equations
ANSWERED 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. 2020-11-06
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
$$Ax+By+Cz=D$$
$$\text{where } A,B,C,D \in R$$
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.