To determine the number of solutions to the given system of linear equations, we can analyze the equations provided:
- \( y = x + 5 \)
- \( y = -x + 5 \)
Next, we can set the two equations equal to each other to find their intersection point:
\[ x + 5 = -x + 5 \]
Now, we simplify this equation:
\[ x + x = 5 - 5 \] \[ 2x = 0 \] \[ x = 0 \]
Now, we substitute \( x = 0 \) back into either of the original equations to find \( y \). We can use the first equation:
\[ y = 0 + 5 = 5 \]
Thus, the point of intersection is \( (0, 5) \).
Since we found exactly one point where the two lines intersect, we conclude that there is exactly 1 solution to the system of equations.
So, the answer is:
1