1. **State the problem:** Solve the system of linear equations: $$2x + y = 19$$ $$3x + 4y = 26$$ 2. **Formula and method:** We can use substitution or elimination to solve this system. Here, we'll use substitution. 3. **Isolate $y$ in the first equation:** $$y = 19 - 2x$$ 4. **Substitute $y$ into the second equation:** $$3x + 4(19 - 2x) = 26$$ 5. **Simplify and solve for $x$:** $$3x + 76 - 8x = 26$$ $$-5x + 76 = 26$$ $$-5x = 26 - 76$$ $$-5x = -50$$ $$x = \frac{-50}{-5} = 10$$ 6. **Substitute $x=10$ back into $y = 19 - 2x$ to find $y$:** $$y = 19 - 2(10) = 19 - 20 = -1$$ 7. **Final answer:** $$x = 10, \quad y = -1$$ This means the solution to the system is the point $(10, -1)$ where both equations intersect.