1. **State the problem:** Solve the system of linear equations: Top-left pair: $$5x - 3y = 4$$ $$-x + y = -2$$ 2. **Use substitution or elimination:** From the second equation, express $y$ in terms of $x$: $$-x + y = -2 \implies y = x - 2$$ 3. **Substitute $y = x - 2$ into the first equation:** $$5x - 3(x - 2) = 4$$ 4. **Simplify:** $$5x - 3x + 6 = 4$$ $$2x + 6 = 4$$ 5. **Isolate $x$:** $$2x = 4 - 6$$ $$2x = -2$$ $$\cancel{2}x = \cancel{2}(-1)$$ $$x = -1$$ 6. **Find $y$ using $y = x - 2$:** $$y = -1 - 2 = -3$$ 7. **Final solution:** $$\boxed{x = -1, y = -3}$$