Determine Whether the Two Systems of Linear Equations Yield the Same

question 174

Multiple Choice

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

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Definitions:

Proton Spin Decoupled

A nuclear magnetic resonance (NMR) technique where the interaction between proton spins is removed or reduced, enhancing spectral resolution.

0-50 Ppm

A concentration range indicating 0 to 50 parts per million, often used to describe the presence of a substance within another substance.

Proton Spin Decoupled

A nuclear magnetic resonance (NMR) technique used to simplify the spectrum and analyze the structure by decoupling the interactions between proton spins.

Proton Spin Decoupled

A nuclear magnetic resonance (NMR) technique used to simplify spectra by removing interaction between proton spins.