c) The difference of two numbers $$ x $$ and $$ y $$ is 3 . (i) Write an equation to represent the difference of the numbers (ii) If $$ y=\frac{2 x}{3} $$, find the values of $$ x $$ and $$ y $$.

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To solve the problem, let's break it down step by step.

### (i) Write an equation to represent the difference of the numbers

The difference of two numbers $$ x $$ and $$ y $$ is given as 3. This can be represented by the equation:

$$
x - y = 3
$$

### (ii) If $$ y = \frac{2x}{3} $$, find the values of $$ x $$ and $$ y $$

We can substitute the expression for $$ y $$ into the equation we found in part (i).

1. Substitute $$ y = \frac{2x}{3} $$ into the equation $$ x - y = 3 $$:

$$
x - \frac{2x}{3} = 3
$$

2. To simplify the left side, we can express $$ x $$ as a fraction:

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

Now, substituting this into the equation gives:

$$
\frac{3x}{3} - \frac{2x}{3} = 3
$$

3. Combine the fractions:

$$
\frac{3x - 2x}{3} = 3
$$

This simplifies to:

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

4. To solve for $$ x $$, multiply both sides by 3:

$$
x = 9
$$

5. Now that we have $$ x $$, we can find $$ y $$ using the equation $$ y = \frac{2x}{3} $$:

$$
y = \frac{2(9)}{3} = \frac{18}{3} = 6
$$

### Final Values

Thus, the values of $$ x $$ and $$ y $$ are:

$$
x = 9, \quad y = 6
$$
The values of $$ x $$ and $$ y $$ are $$ x = 9 $$ and $$ y = 6 $$.

c) The difference of two numbers \( x \) and \( y \) is 3 . (i) Write an equation to represent the difference of the numbers (ii) If \( y=\frac{2 x}{3} \), find the values of \( x \) and \( y \).

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