1. **State the problem:** Solve the system of linear equations: $$3kx - 4y = 2$$ $$2 - 5y = x$$ 2. **Rewrite the second equation to express $x$ in terms of $y$: ** $$x = 2 - 5y$$ 3. **Substitute $x$ from the second equation into the first equation:** $$3k(2 - 5y) - 4y = 2$$ 4. **Distribute $3k$:** $$6k - 15ky - 4y = 2$$ 5. **Group terms with $y$:** $$-15ky - 4y = 2 - 6k$$ 6. **Factor out $y$:** $$y(-15k - 4) = 2 - 6k$$ 7. **Solve for $y$:** $$y = \frac{2 - 6k}{-15k - 4}$$ 8. **Substitute $y$ back into $x = 2 - 5y$ to find $x$:** $$x = 2 - 5 \times \frac{2 - 6k}{-15k - 4} = 2 + \frac{5(2 - 6k)}{15k + 4}$$ 9. **Simplify $x$:** $$x = \frac{2(15k + 4)}{15k + 4} + \frac{5(2 - 6k)}{15k + 4} = \frac{30k + 8 + 10 - 30k}{15k + 4} = \frac{18}{15k + 4}$$ **Final solution:** $$x = \frac{18}{15k + 4}, \quad y = \frac{2 - 6k}{-15k - 4}$$ This solution expresses $x$ and $y$ in terms of the parameter $k$.