To solve the system of equations:
- \( x + y = 17 \) (Equation 1)
- \( x - y = -3 \) (Equation 2)
We can use the method of elimination or substitution. Here, we'll use elimination.
First, we can add both equations together:
\[ (x + y) + (x - y) = 17 + (-3) \]
This simplifies to:
\[ 2x = 14 \]
Now, divide both sides by 2:
\[ x = 7 \]
Next, we can substitute the value of \( x \) back into one of the original equations to find \( y \). We'll use Equation 1:
\[ 7 + y = 17 \]
Subtract 7 from both sides:
\[ y = 10 \]
Thus, the solution to the system of equations is:
\[ x = 7, \quad y = 10 \]
So, the final answer is \( (x, y) = (7, 10) \).