Determine whether the two systems of linear equations yield the same solutions.
If so, find the solutions using matrices.
$\begin{array} { l }
\left\{ \begin{aligned}
x + y - 9 z & = - 67 \
y + 5 z & = 31 \
z & = 7
\end{aligned} \right. \
\left\{ \begin{aligned}
x - 9 y + 6 z & = 76 \
y - 9 z & = - 67 \
z & = 7
\end{aligned} \right.
\end{array}$
A) $x = 0 , y = - 4 , z = 7$
B) $x = 0 , y = 4 , z = 7$
C) $x = 4 , y = 7 , z = 0$
D) $x = - 4 , y = 7 , z = 0$
E) The systems yield different solutions.

Question

Determine whether the two systems of linear equations yield the same solutions.
If so, find the solutions using matrices.
$\begin{array} { l } 
\left\{ \begin{aligned}
x + y - 9 z & = - 67 \
y + 5 z & = 31 \
z & = 7
\end{aligned} \right. \
\left\{ \begin{aligned}
x - 9 y + 6 z & = 76 \
y - 9 z & = - 67 \
z & = 7
\end{aligned} \right.
\end{array}$
A) $x = 0 , y = - 4 , z = 7$
B) $x = 0 , y = 4 , z = 7$
C) $x = 4 , y = 7 , z = 0$
D) $x = - 4 , y = 7 , z = 0$
E) The systems yield different solutions.

Quizplus · Accepted Answer

The systems yield different solutions because substituting $z = 7$ into each system yields different equations for $x$ and $y$, indicating that they do not have the same solution set.

Determine Whether the Two Systems of Linear Equations Yield the Same