1. **State the problem:** Solve the first system of linear equations: $$y = 3x - 5$$ $$5x + 4y = -3$$ 2. **Use substitution method:** Since $y$ is already expressed in terms of $x$ in the first equation, substitute $y = 3x - 5$ into the second equation. 3. **Substitute and simplify:** $$5x + 4(3x - 5) = -3$$ $$5x + 12x - 20 = -3$$ $$17x - 20 = -3$$ 4. **Isolate $x$:** $$17x = -3 + 20$$ $$17x = 17$$ $$x = \frac{\cancel{17}}{\cancel{17}} = 1$$ 5. **Find $y$ using $x=1$:** $$y = 3(1) - 5 = 3 - 5 = -2$$ 6. **Final answer:** $$x = 1, \quad y = -2$$ This is the solution to the first system of equations.