1. **State the problem:** Solve the system of equations: $$3x + 2y = 19$$ $$2x - y = 1$$ 2. **Formula and rules:** To solve a system of linear equations, we can use substitution or elimination. Here, we use substitution. 3. **Isolate $y$ in the second equation:** $$2x - y = 1 \implies y = 2x - 1$$ 4. **Substitute $y = 2x - 1$ into the first equation:** $$3x + 2(2x - 1) = 19$$ 5. **Simplify:** $$3x + 4x - 2 = 19$$ $$7x - 2 = 19$$ 6. **Add 2 to both sides:** $$7x - 2 + 2 = 19 + 2$$ $$7x = 21$$ 7. **Divide both sides by 7:** $$\cancel{7}x = \frac{21}{\cancel{7}}$$ $$x = 3$$ 8. **Substitute $x=3$ back into $y = 2x - 1$:** $$y = 2(3) - 1 = 6 - 1 = 5$$ 9. **Solution:** $$x = 3, y = 5$$ 10. **Answer choice:** b. $x=3, y=5$ --- 11. **Second problem:** Two lines in a linear system have the same slope but different intercepts. 12. **Rule:** Lines with the same slope but different intercepts are parallel and never intersect. 13. **Conclusion:** The system has **no solutions** because the lines do not intersect.