1. **State the problem:** Solve the system of linear equations: $$y = 4x + 13$$ $$y = 6x + 19$$ 2. **Use the substitution or elimination method:** Since both equations equal $y$, set them equal to each other: $$4x + 13 = 6x + 19$$ 3. **Solve for $x$:** Subtract $4x$ from both sides: $$\cancel{4x} + 13 = 6x + 19 - \cancel{4x}$$ $$13 = 2x + 19$$ Subtract 19 from both sides: $$13 - 19 = 2x + \cancel{19} - \cancel{19}$$ $$-6 = 2x$$ Divide both sides by 2: $$\frac{-6}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ $$-3 = x$$ 4. **Find $y$ by substituting $x = -3$ into one of the original equations:** Using $y = 4x + 13$: $$y = 4(-3) + 13 = -12 + 13 = 1$$ 5. **Final answer:** $$\boxed{(x, y) = (-3, 1)}$$