1. **State the problem:** Solve the system of equations: $$3x - 5x = 11 - 5$$ $$x + y = 1$$ 2. **Simplify the first equation:** $$3x - 5x = -2x$$ $$11 - 5 = 6$$ So the equation becomes: $$-2x = 6$$ 3. **Solve for $x$:** Divide both sides by $-2$: $$\cancel{-2}x = \frac{6}{\cancel{-2}}$$ $$x = -3$$ 4. **Substitute $x = -3$ into the second equation:** $$x + y = 1$$ $$-3 + y = 1$$ 5. **Solve for $y$:** Add 3 to both sides: $$-3 + y + 3 = 1 + 3$$ $$y = 4$$ 6. **Final solution:** $$x = -3, \quad y = 4$$ These values satisfy both equations.