Explanation:

- We have two key equations: \(x + y = 10\) and \(2xy = 48\).

- From the first equation, express one variable in terms of the other: \(x = 10 - y\).

- Substitute \(x = 10 - y\) into \(2xy = 48\):

$$

2(10-y)y = 48 \quad \implies \quad 20y - 2y^2 = 48.

$$

- Rearrange to form:

$$

2y^2 - 20y + 48 = 0.

$$

- Simplify:

$$

y^2 - 10y + 24 = 0.

$$

- Factor this quadratic:

$$

(y - 6)(y - 4) = 0.

$$

- Therefore, \(y = 6\) or \(y = 4\). Since \(x > y\), it must be \(y = 4\).

- So \(x = 10 - y = 6\).

- Calculate \(2x - y = 2(6) - 4 = 12 - 4 = 8\).

Thus, the correct option is Option:2, 8 .