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:
\[
x = \frac{5y + 6}{3}
\]
\[
y = \frac{3x - 6}{5}
\]
