1. **State the problem:** Solve the system of linear equations labeled (l): $$3x - y = 4$$ $$5x + 4y = 52$$ 2. **Method:** We will use the substitution or elimination method. Here, elimination is convenient. 3. **Eliminate $y$:** Multiply the first equation by 4 to align coefficients of $y$: $$4(3x - y) = 4(4) \Rightarrow 12x - 4y = 16$$ 4. **Add to second equation:** $$12x - 4y = 16$$ $$5x + 4y = 52$$ Add both equations: $$12x - 4y + 5x + 4y = 16 + 52$$ $$ (12x + 5x) + (-4y + 4y) = 68$$ $$17x + \cancel{-4y + 4y} = 68$$ 5. **Solve for $x$:** $$17x = 68$$ $$x = \frac{68}{17}$$ $$x = 4$$ 6. **Substitute $x=4$ into first equation:** $$3(4) - y = 4$$ $$12 - y = 4$$ 7. **Solve for $y$:** $$-y = 4 - 12$$ $$-y = -8$$ $$y = 8$$ **Final answer:** $$x = 4, \quad y = 8$$