Solve: `{:(x + y = 17),(x - y = 1):}`

Answer

To solve the system of equations given by:

1. \( x + y = 17 \) (Equation 1)
2. \( x - y = 1 \) (Equation 2)

we can follow these steps:

### Step 1: Express one variable in terms of the other
From Equation 2, we can express \( y \) in terms of \( x \).

\[ x - y = 1 \implies y = x - 1 \]

### Step 2: Substitute the expression into the other equation
Now, we will substitute the expression for \( y \) from Step 1 into Equation 1.

\[ x + (x - 1) = 17 \]

### Step 3: Simplify the equation
Now, simplify the equation:

\[ x + x - 1 = 17 \implies 2x - 1 = 17 \]

### Step 4: Solve for \( x \)
Next, we will isolate \( x \):

\[ 2x - 1 + 1 = 17 + 1 \implies 2x = 18 \]
\[ x = \frac{18}{2} = 9 \]

### Step 5: Substitute back to find \( y \)
Now that we have \( x \), we can find \( y \) using the expression we found in Step 1:

\[ y = x - 1 = 9 - 1 = 8 \]

### Conclusion
The solution to the system of equations is:

\[ x = 9, \quad y = 8 \]