1. **State the problem:** We need to solve the system of simultaneous linear equations: $$y = 5x - 2$$ $$y = 10x - 4$$ 2. **Use the method of equating values of $y$:** Since both expressions equal $y$, set them equal to each other: $$5x - 2 = 10x - 4$$ 3. **Solve for $x$:** Subtract $5x$ from both sides: $$\cancel{5x} - 2 = 10x - \cancel{5x} - 4 \implies -2 = 5x - 4$$ Add 4 to both sides: $$-2 + 4 = 5x - 4 + 4 \implies 2 = 5x$$ Divide both sides by 5: $$\frac{2}{\cancel{5}} = x \frac{\cancel{5}}{5} \implies x = \frac{2}{5}$$ 4. **Find $y$ by substituting $x = \frac{2}{5}$ into one of the original equations:** Using $y = 5x - 2$: $$y = 5 \times \frac{2}{5} - 2 = 2 - 2 = 0$$ 5. **Final answer:** The solution to the system is: $$\boxed{\left(\frac{2}{5}, 0\right)}$$ This means the two lines intersect at the point $\left(\frac{2}{5}, 0\right)$.