Form the pair of linear equations for the following problems and find their solution by substitution method.
The difference between two numbers is 26 and one number is three times the other. Find them.

Answer

To solve the problem, we need to form a pair of linear equations based on the information provided and then solve them using the substitution method.

### Step 1: Define the Variables
Let:
- \( x \) = the first number
- \( y \) = the second number

### Step 2: Form the Equations
From the problem, we have two statements:
1. The difference between the two numbers is 26.
This can be expressed as:
\[ x - y = 26 \quad \text{(Equation 1)} \]

2. One number is three times the other.
Assuming \( x \) is the larger number, we can express this as:
\[ x = 3y \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1
Now we will substitute the value of \( x \) from Equation 2 into Equation 1:
\[ 3y - y = 26 \]

### Step 4: Simplify and Solve for \( y \)
Combine like terms:
\[ 2y = 26 \]
Now, divide both sides by 2:
\[ y = 13 \]

### Step 5: Substitute \( y \) back to find \( x \)
Now that we have \( y \), we can substitute it back into Equation 2 to find \( x \):
\[ x = 3y = 3 \times 13 = 39 \]

### Conclusion
The two numbers are:
- \( x = 39 \)
- \( y = 13 \)

### Final Answer
The two numbers are 39 and 13.

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