1. **Problem:** Solve the system of equations $$5x - 19 = y$$ $$3x - 11 = y$$ 2. **Method:** Since both expressions equal $y$, set them equal to each other: $$5x - 19 = 3x - 11$$ 3. **Solve for $x$:** $$5x - 19 = 3x - 11$$ $$5x - \cancel{19} + 19 = 3x - \cancel{11} + 11$$ $$5x = 3x + 8$$ $$5x - 3x = 8$$ $$2x = 8$$ $$x = \frac{8}{2}$$ $$x = 4$$ 4. **Find $y$ by substituting $x=4$ into one of the original equations:** $$y = 5(4) - 19$$ $$y = 20 - 19$$ $$y = 1$$ **Final answer:** $$x = 4, \quad y = 1$$ This method is called the substitution or equalization method, where you set the expressions for $y$ equal and solve for $x$, then back-substitute to find $y$.