Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices. $\left\{ \begin{aligned}
x - 8 y - 8 z & = - 36 \
y + 2 z & = 7 \
z & = 2
\end{aligned} \right.$ $\left\{ \begin{aligned}
x - 7 y + 5 z & = - 7 \
y + 2 z & = 7 \
z & = 2
\end{aligned} \right.$
A)x = 4, y = 3, z = 2
B)x = -4, y = -3, z = 2
C)x = -3, y = 2, z = 4
D)x = 3, y = 2, z = 4
E)The systems yield different solutions.

Question

Quizplus · Accepted Answer

Both systems have the same second and third equations. Solving for z = 2 and substituting into y + 2z = 7 gives y = 3. Substituting y = 3 and z = 2 into the first equation of each system gives x = 4 for both, confirming they yield the same solution: x = 4, y = 3, z = 2.

Determine Whether the Two Systems of Linear Equations Yield the Same