Question: Use both of the equations below to work out the value of $b$.
$$\frac{5a - 3}{9} = 3$$
$$7b - 1 = a - 21$$
1. **State the problem:** We are given two equations:
$$\frac{5a - 3}{9} = 3$$
and
$$7b - 1 = a - 21$$
We need to find the value of $b$.
2. **Use the first equation to find $a$: **
Multiply both sides of the first equation by 9 to eliminate the denominator:
$$\cancel{9} \times \frac{5a - 3}{\cancel{9}} = 3 \times 9$$
which simplifies to:
$$5a - 3 = 27$$
3. **Solve for $a$: **
Add 3 to both sides:
$$5a - 3 + 3 = 27 + 3$$
$$5a = 30$$
Divide both sides by 5:
$$\frac{5a}{\cancel{5}} = \frac{30}{\cancel{5}}$$
$$a = 6$$
4. **Substitute $a = 6$ into the second equation: **
$$7b - 1 = 6 - 21$$
Simplify the right side:
$$7b - 1 = -15$$
5. **Solve for $b$: **
Add 1 to both sides:
$$7b - 1 + 1 = -15 + 1$$
$$7b = -14$$
Divide both sides by 7:
$$\frac{7b}{\cancel{7}} = \frac{-14}{\cancel{7}}$$
$$b = -2$$
**Final answer:**
$$b = -2$$