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

Forms of linear equations

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 $$y = mx + b$$.

2021-05-12

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 $$y=mx+b.$$
$$akx+bky=dk$$
$$bky=-akx+dk$$
$$y=-(ak/bk)x+dk/bk$$