Topic:Change of subject of formula Let's Take number number 1-20

$$y - 8 = x + 8 - 8$$ $$y - 8 = x$$

$$x = y - 8$$

The subject is $\boxed{x = y - 8}$.

2) Given formula: $y = x - 3$. Make $x$ the subject.

$$y + 3 = x - 3 + 3$$ $$y + 3 = x$$

$$x = y + 3$$

The subject is $\boxed{x = y + 3}$.

3) Given formula: $b = a + c$. Make $a$ and $c$ the subject.

a) Make $a$ the subject:

$$b - c = a + c - c$$ $$b - c = a$$

$$a = b - c$$

The subject is $\boxed{a = b - c}$.

b) Make $c$ the subject:

$$b - a = a + c - a$$ $$b - a = c$$

$$c = b - a$$

The subject is $\boxed{c = b - a}$.

4) Given formula: $y = 3x$. Make $x$ the subject.

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

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

The subject is $\boxed{x = \frac{y}{3}}$.

5) Given formula: $y = \frac{x}{4}$. Make $x$ the subject.

$$y \times 4 = \frac{x}{4} \times 4$$ $$4y = x$$

$$x = 4y$$

The subject is $\boxed{x = 4y}$.

6) Given formula: $b = ac$. Make $a$ and $c$ the subject.

a) Make $a$ the subject:

$$\frac{b}{c} = \frac{ac}{c}$$ $$\frac{b}{c} = a$$

$$a = \frac{b}{c}$$

The subject is $\boxed{a = \frac{b}{c}}$.

b) Make $c$ the subject:

$$\frac{b}{a} = \frac{ac}{a}$$ $$\frac{b}{a} = c$$

$$c = \frac{b}{a}$$

The subject is $\boxed{c = \frac{b}{a}}$.

7) Given formula: $n = 5ax$. Make $a$ and $x$ the subject.

a) Make $a$ the subject:

$$\frac{n}{5x} = \frac{5ax}{5x}$$ $$\frac{n}{5x} = a$$

$$a = \frac{n}{5x}$$

The subject is $\boxed{a = \frac{n}{5x}}$.

b) Make $x$ the subject:

$$\frac{n}{5a} = \frac{5ax}{5a}$$ $$\frac{n}{5a} = x$$

$$x = \frac{n}{5a}$$

The subject is $\boxed{x = \frac{n}{5a}}$.

8) Given formula: $\frac{x}{y} = 9$. Make $x$ the subject.

$$\frac{x}{y} \times y = 9 \times y$$ $$x = 9y$$

The subject is $\boxed{x = 9y}$.