Determine Whether the Two Systems of Linear Equations Yield the Same

question 8

Multiple Choice

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.
$$\begin{aligned}\left\{ \begin{aligned}x + 9 y - 2 z & = 41 \\y - 7 z & = 46 \\z & = - 6\end{aligned} \right.\\\left\{ \begin{aligned}x + 4 y + 2 z & = - 3 \\y + 5 z & = - 26 \\z & = - 6\end{aligned} \right.\end{aligned}$$

• A) \(x = - 7 , y = 4 , z = - 6\)
• B) \(x = 7 , y = - 4 , z = - 6\)
• C) \(x = - 4 , y = - 6 , z = - 7\)
• D) \(x = 4 , y = - 6 , z = - 7\)
• E) The systems yield different solutions.

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Definitions:

Anvil

In non-biological contexts, an anvil is a heavy iron block used in metalworking. In the context of the ear, it refers to the incus, a small anvil-shaped bone in the middle ear that helps transmit sound vibrations.

Stirrup

The stirrup, or stapes, is a small bone in the middle ear that plays a key role in the transmission of sound vibrations to the inner ear.

Middle Ear

A part of the ear between the eardrum and the inner ear, containing three small bones that help transmit sound.

Sound Wave

A type of wave that is an audible vibration that travels through air or other media and is perceived by the human ear.