Solve for b given the equations a2 = 81 and 2a + b = 20.

We are given the equation:

$$a^2 = 81$$

To find $a$, take the square root of both sides:

$$a = \pm\sqrt{81}$$

This gives two possible values for $a$:

$$a = 9 \quad \text{or} \quad a = -9$$

The second equation is:

$$2a + b = 20$$

Case 1: If $a = 9$
Substitute $a=9$ into the second equation:

$$2(9) + b = 20$$ $$18 + b = 20$$

Subtract 18 from both sides:

$$b = 20 - 18$$ $$b = 2$$

Case 2: If $a = -9$
Substitute $a=-9$ into the second equation:

$$2(-9) + b = 20$$ $$-18 + b = 20$$

Add 18 to both sides:

$$b = 20 + 18$$ $$b = 38$$

Therefore, there are two possible values for $b$.

The final answers are $\text{b = 2 or b = 38}$.