Kyran Hudson
2020-11-05
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.

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avortarF

Answered 2020-11-06
Author has **113** answers

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.

The equations of a linear system with 3 variables are of the form:

A,B,C,D can have the values:

In this particular case, the equation is written:

We add y+n on both sides and we have:

Thus it is possible to have equations in the form

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