Solve the System $$\begin{aligned}b + 5 c & = 7 \\12 a - c & = 18 \\- 6 a + 3 b & = - 19\end{aligned}$$

question 45

Multiple Choice

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
- $$\begin{aligned}b + 5 c & = 7 \\12 a - c & = 18 \\- 6 a + 3 b & = - 19\end{aligned}$$

• A) \(\{ ( - 1,157 , - 30 ) \}\)
• B) No solution; inconsistent
• C) \(\left\{ \left( \frac { 5 } { 3 } , - 3,2 \right) \right\}\)
• D) \(\{ ( 2 , - 23,6 ) \}\)

---

Definitions:

Resonance Hybrid

A composite representation of a molecule that cannot be depicted accurately by a single structural formula, illustrating electron delocalization.

Aromatic

Describes organic compounds that contain one or more planar rings of atoms with delocalized pi electrons, following Huckel's rule.

Nodal Planes

Imaginary planes in an atom or molecule where the probability of finding an electron is zero, often associated with molecular orbitals.

P Orbitals

Atomic orbitals shaped like dumbbells, consisting of regions where there's a high probability of finding an electron outside the nucleus, pivotal in chemical bonding and valence.