Determine whether the two systems of linear equations yield the same solutions.If so, find the solutions using matrices. $$\left\{ \begin{aligned}
x - y - 6 z & = - 33 \
y + 3 z & = 18 \
z & = 4
\end{aligned} \right.$$ $$\left\{ \begin{array} { r l r }
x - 7 y - 3 z & = - 57 \
y - 9 z & = - 30 \
z & = 4
\end{array} \right.$$
A)x = -3, y = 6, z = 4
B)The systems yield different solutions.
C)x = 3, y = 4, z = -3
D)x = 3, y = -6, z = 4
E)x = 6, y = 4, z = -3

Question

Determine whether the two systems of linear equations yield the same solutions.If so, find the solutions using matrices. $$\left\{ \begin{aligned}
x - y - 6 z & = - 33 \
y + 3 z & = 18 \
z & = 4
\end{aligned} \right.$$ $$\left\{ \begin{array} { r l r } 
x - 7 y - 3 z & = - 57 \
y - 9 z & = - 30 \
z & = 4
\end{array} \right.$$
A)x = -3, y = 6, z = 4
B)The systems yield different solutions.
C)x = 3, y = 4, z = -3
D)x = 3, y = -6, z = 4
E)x = 6, y = 4, z = -3

Quizplus · Accepted Answer

Given that both systems have $z = 4$, we can substitute this value into the other equations to find $x$ and $y$. For the first system, substituting $z = 4$ into the second equation gives $y + 3(4) = 18$, which simplifies to $y = 6$. Substituting $y = 6$ and $z = 4$ into the first equation gives $x - 6 - 6(4) = -33$, which simplifies to $x = -3$. For the second system, substituting $z = 4$ into the second equation gives $y - 9(4) = -30$, which also simplifies to $y = 6$. Substituting $y = 6$ and $z = 4$ into the first equation gives $x - 7(6) - 3(4) = -57$, which also simplifies to $x = -3$. Therefore, both systems yield the same solution: $x = -3$, $y = 6$, $z = 4$.

Determine Whether the Two Systems of Linear Equations Yield the Same