For what value of a does the system of equations 2x + ay = 1 and 3x − 5y = 7 have a unique solution?

The given system of equations is:

$$2x + ay = 1$$ $$3x - 5y = 7$$

Comparing these with the standard form $a_1x + b_1y = c_1$ and $a_2x + b_2y = c_2$, we have:
$a_1 = 2$, $b_1 = a$
$a_2 = 3$, $b_2 = -5$

For a system of linear equations to have a unique solution, the ratio of the coefficients of $x$ must not be equal to the ratio of the coefficients of $y$.

$$\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$$

Substitute the values from Step 1 into the condition from Step 2:

$$\frac{2}{3} \neq \frac{a}{-5}$$

To solve for $a$, multiply both sides of the inequality by $-5$:

$$-5 \times \frac{2}{3} \neq a$$ $$-\frac{10}{3} \neq a$$

The condition for a unique solution is $a \neq -\frac{10}{3}$.
Looking at the options:

(a) $a = \frac{10}{3}$

(b) $a \neq -\frac{10}{3}$

(c) $a = 10$

(d) $a \neq 10$

The correct option is (b).

The final answer is $\boxed{\text{(b) } a \neq -\frac{10}{3}}$.