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
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asked 2020-11-05
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.

Answers (1)

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.
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