Step-by-Step Solution:
1. Start with the two given equations:
(Eq. 1) $\(2 x-y=10\)$
(Eq. 2) $\(\frac{x}{y}=3\)$
2. Isolate $y$ in the second equation:

From $\frac{x}{y}=3$, we can multiply both sides by $y$ to get:

$$
\(x=3 y\)
$$


Now, divide by 3 to express $y$ in terms of $x$ :

$$
\(y=\frac{x}{3}\)
$$

3. Substitute this expression for $y$ into the first equation:

$$
\(2 x-\left(\frac{x}{3}\right)=10\)
$$

4. Solve for $x$ :

To clear the fraction, multiply every term in the equation by 3 :

$$
\(\begin{gathered}
3(2 x)-3\left(\frac{x}{3}\right)=3(10) \\
6 x-x=30 \\
5 x=30
\end{gathered}\)
$$

$$
\(x=6\)
$$


Check your work:
If $x=6$, then $\(y=\frac{6}{3}=2\)$.

Plugging these into the first equation: $\(2(6)-2=12-2=10\)$. This matches the original equation.

Correct Option:
D. 6