1. The problem is to find the value of $y$ in the system of linear equations: $$10x - y = 0$$ $$x + 5y = 51$$ 2. We will use substitution or elimination to solve the system. Here, substitution is straightforward. 3. From the first equation, solve for $y$: $$10x - y = 0 \implies y = 10x$$ 4. Substitute $y = 10x$ into the second equation: $$x + 5(10x) = 51$$ $$x + 50x = 51$$ $$51x = 51$$ 5. Solve for $x$: $$x = \frac{51}{51} = 1$$ 6. Substitute $x = 1$ back into $y = 10x$: $$y = 10 \times 1 = 10$$ 7. Therefore, the value of $y$ is 10.