Solve the following pair of linear equations by the substitution method:
`s-t =3`
`(s)/(3) + (t)/(2)=6`

Answer

To solve the given pair of linear equations using the substitution method, we will follow these steps:

### Step 1: Write down the equations
The given equations are:
1. \( s - t = 3 \) (Equation 1)
2. \( \frac{s}{3} + \frac{t}{2} = 6 \) (Equation 2)

### Step 2: Solve Equation 1 for one variable
From Equation 1, we can express \( s \) in terms of \( t \):
\[ s = t + 3 \]

### Step 3: Substitute \( s \) in Equation 2
Now, we will substitute the expression for \( s \) into Equation 2:
\[ \frac{(t + 3)}{3} + \frac{t}{2} = 6 \]

### Step 4: Eliminate the fractions
To eliminate the fractions, we can find a common denominator. The least common multiple of 3 and 2 is 6. Multiply the entire equation by 6:
\[ 6 \cdot \left(\frac{(t + 3)}{3}\right) + 6 \cdot \left(\frac{t}{2}\right) = 6 \cdot 6 \]
This simplifies to:
\[ 2(t + 3) + 3t = 36 \]

### Step 5: Simplify the equation
Now, distribute and combine like terms:
\[ 2t + 6 + 3t = 36 \]
\[ 5t + 6 = 36 \]

### Step 6: Solve for \( t \)
Subtract 6 from both sides:
\[ 5t = 30 \]
Now, divide by 5:
\[ t = 6 \]

### Step 7: Substitute back to find \( s \)
Now that we have the value of \( t \), we can substitute it back into the expression for \( s \):
\[ s = t + 3 = 6 + 3 = 9 \]

### Step 8: Write the final solution
Thus, the solution to the system of equations is:
\[ s = 9, \quad t = 6 \]