Solve the system of equations below: $- 6 x + y + 7 z = 20$ $7 x - 2 y - 9 z = - 25$
A) $( - c - 3 , c + 2 , c )$
B) $( c - 3 , - c + 2 , c )$
C) $( c + 2 , - c - 3 , c )$
D) $( - c + 2 , c - 3 , c )$
E) $( - 3 c + 2 , c - 1 , c )$

Question

Quizplus · Accepted Answer

The system of equations given is underdetermined, meaning it has more unknowns than equations, which typically results in an infinite number of solutions that can be expressed in terms of a parameter, in this case, $c$. By solving the system, we can express $x$, $y$, and $z$ in terms of $c$. The correct representation that fits the given system of equations, after manipulation and substitution, is $(c - 3, -c + 2, c)$, which corresponds to choice B. This choice correctly aligns the variables with the parameter $c$ in a way that is consistent with the operations needed to solve the system of equations.

Solve the System of Equations Below −6x+y+7z=20- 6 x + y + 7 z = 20−6x+y+7z=20

Solve the System of Equations Below $- 6 x + y + 7 z = 20$