Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.
$\left\{ \begin{aligned} x + y - 9 z & = - 67 \ y + 5 z & = 31 \ z & = 7 \end{aligned} \right.$
$\left\{ \begin{aligned} x - 9 y + 6 z & = 76 \ y - 9 z & = - 67 \ z & = 7 \end{aligned} \right.$
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

Quizplus · Accepted Answer

The third equation in both systems directly gives $z = 7$, but substituting $z = 7$ into the other equations of each system will yield different values for $x$ and $y$, indicating the systems do not yield the same solution set.

Determine Whether the Two Systems of Linear Equations Yield the Same