Answer :

Answer:

Step-by-step explanation:To solve the equation \(\frac{x - 2}{5} = \frac{y}{3}\) for \(x\) and \(y\), we need to find the relationship between \(x\) and \(y\). Let's manipulate the equation step-by-step:

Given:

\[

\frac{x - 2}{5} = \frac{y}{3}

\]

1. Cross-multiply to eliminate the fractions:

\[

3(x - 2) = 5y

\]

2. Distribute the 3 on the left side:

\[

3x - 6 = 5y

\]

3. Solve for \(x\):

\[

3x = 5y + 6

\]

\[

x = \frac{5y + 6}{3}

\]

4. Alternatively, solve for \(y\):

\[

5y = 3x - 6

\]

\[

y = \frac{3x - 6}{5}

\]

So, the equations expressing \(x\) and \(y\) in terms of each other are:

\[

x = \frac{5y + 6}{3}

\]

\[

y = \frac{3x - 6}{5}

\]