Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.
$$\begin{array} { r }
\left\{ \begin{aligned}
x + 5 y - 5 z & = 42 \
y - 9 z & = 48 \
z & = - 5 \
\{ x + 8 y - 3 z & = 31 \
y + 5 z & = - 22 \
z & = - 5
\end{aligned} \right.
\end{array}$$
A) $x = 2 , y = 3 , z = - 5$
B) $x = - 2 , y = - 3 , z = - 5$
C) $x = - 3 , y = - 5 , z = 2$
D) $x = 3 , y = - 5 , z = 2$
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.
$$\begin{array} { r } 
\left\{ \begin{aligned}
x + 5 y - 5 z & = 42 \
y - 9 z & = 48 \
z & = - 5 \
\{ x + 8 y - 3 z & = 31 \
y + 5 z & = - 22 \
z & = - 5
\end{aligned} \right.
\end{array}$$
A) $x = 2 , y = 3 , z = - 5$
B) $x = - 2 , y = - 3 , z = - 5$
C) $x = - 3 , y = - 5 , z = 2$
D) $x = 3 , y = - 5 , z = 2$
E) The systems yield different solutions.

Quizplus · Accepted Answer

The third equation in both systems directly gives $z = -5$. Substituting $z = -5$ into the second equation of each system yields different values for $y$: $y - 9(-5) = 48$ gives $y = 3$ for the first system, and $y + 5(-5) = -22$ gives $y = -3$ for the second system. Since $y$ differs, the systems yield different solutions.

Determine Whether the Two Systems of Linear Equations Yield the Same