To solve the system of equations:
- \( x + 3y = 15 \) (Equation 1)
- \( 3x + 2y = 10 \) (Equation 2)
We can use the substitution or elimination method. Here, let's use the substitution method.
From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 15 - 3y \]
Next, we will substitute this expression for \( x \) into Equation 2:
\[ 3(15 - 3y) + 2y = 10 \]
Expanding this, we get:
\[ 45 - 9y + 2y = 10 \]
Combining like terms:
\[ 45 - 7y = 10 \]
Next, isolate \( y \) by subtracting 45 from both sides:
\[ -7y = 10 - 45 \]
This simplifies to:
\[ -7y = -35 \]
Now, divide both sides by -7:
\[ y = \frac{-35}{-7} = 5 \]
Thus, the value of \( y \) for the solution to the system is:
\[ \boxed{5} \]