1. **State the problem:** Solve the system of linear equations: $$y = 5x$$ $$y = 7x - 16$$ 2. **Set the equations equal to each other:** Since both expressions equal $y$, we can set them equal: $$5x = 7x - 16$$ 3. **Isolate $x$:** Subtract $7x$ from both sides: $$5x - 7x = 7x - 7x - 16$$ $$\cancel{5x} - \cancel{7x} = -16$$ $$-2x = -16$$ 4. **Solve for $x$:** Divide both sides by $-2$: $$\frac{-2x}{\cancel{-2}} = \frac{-16}{\cancel{-2}}$$ $$x = 8$$ 5. **Find $y$:** Substitute $x=8$ into one of the original equations, for example $y=5x$: $$y = 5(8) = 40$$ 6. **Final answer:** The solution to the system is: $$(x, y) = (8, 40)$$