1. We are given two systems of linear equations to solve for $x$ and $y$. 2. First system: $$\begin{cases} 4x - y = 1 \\ 2x + 3y = 11 \end{cases}$$ 3. From the first equation, express $y$ in terms of $x$: $$y = 4x - 1$$ 4. Substitute $y = 4x - 1$ into the second equation: $$2x + 3(4x - 1) = 11$$ 5. Simplify: $$2x + 12x - 3 = 11$$ $$14x - 3 = 11$$ 6. Add 3 to both sides: $$14x = 14$$ 7. Divide both sides by 14: $$x = \frac{\cancel{14}x}{\cancel{14}} = 1$$ 8. Substitute $x=1$ back into $y = 4x - 1$: $$y = 4(1) - 1 = 3$$ 9. Solution for the first system is: $$\boxed{(x,y) = (1,3)}$$ 10. Second system: $$\begin{cases} 5x + y = 9 \\ 10x - 7y = -18 \end{cases}$$ 11. From the first equation, express $y$: $$y = 9 - 5x$$ 12. Substitute into the second equation: $$10x - 7(9 - 5x) = -18$$ 13. Simplify: $$10x - 63 + 35x = -18$$ $$45x - 63 = -18$$ 14. Add 63 to both sides: $$45x = 45$$ 15. Divide both sides by 45: $$x = \frac{\cancel{45}x}{\cancel{45}} = 1$$ 16. Substitute $x=1$ back into $y = 9 - 5x$: $$y = 9 - 5(1) = 4$$ 17. Solution for the second system is: $$\boxed{(x,y) = (1,4)}$$