5**Question:** A quantum materials physicist is investigating the energy states of electrons in a topological superconductor. Let $h$ represent the energy in electronvolts (eV) of an electron in state A, and $k$ represent the energy in eV of an electron in state B. If the physicist finds that $5h + 3k = 15$ and $2h - k = 4$, determine the values of $h$ and $k$.

["Question: A quantum materials physicist is investigating the energy states of electrons in a topological superconductor. Let $h$ represent the energy in electronvolts (eV) of an electron in state A, and $k$ represent the energy in eV of an electron in state B. If the physicist finds that\n$$\n5h + 3k = 15 \quad \ ext{and} \quad 2h - k = 4,\n$$\ndetermine the values of $h$ and $k$.", "To solve this system of equations, we use substitution and elimination. Start with the second equation:\n$$\n2h - k = 4\n$$\nSolve for $k$:\n$$\nk = 2h - 4\n$$", "Now substitute $k = 2h - 4$ into the first equation:\n$$\n5h + 3(2h - 4) = 15\n$$\nExpand and simplify:\n$$\n5h + 6h - 12 = 15\n\Rightarrow 11h - 12 = 15\n\Rightarrow 11h = 27\n\Rightarrow h = \frac{27}{11}\n$$", "Now substitute $h = \frac{27}{11}$ back into $k = 2h - 4$:\n$$\nk = 2\left(\frac{27}{11}\right) - 4 = \frac{54}{11} - \frac{44}{11} = \frac{10}{11}\n$$", "Thus, the energy values are:\n$$\nh = \frac{27}{11}~\ ext{eV}, \quad k = \frac{10}{11}~\ ext{eV}\n$$", "These results may reveal quantized energy levels and topological order in the superconductor, offering insight into exotic electron behavior critical for quantum computing applications.", "This solution combines experimental data with algebraic precision, demonstrating how quantum physicists use mathematical modeling to decode complex material properties.", "Answer: $h = \frac{27}{11}~\ ext{eV}, \quad k = \frac{10}{11}~\ ext{eV}$"]