To find the number of solutions to the system of equations given by:
- \( y = x + 5 \)
- \( y = -x + 5 \)
we can solve for the point(s) of intersection.
Set the two equations equal to each other:
\[ x + 5 = -x + 5 \]
Now, add \( x \) to both sides:
\[ x + x + 5 = 5 \]
This simplifies to:
\[ 2x + 5 = 5 \]
Now, subtract 5 from both sides:
\[ 2x = 0 \]
Now, divide by 2:
\[ x = 0 \]
Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \):
Using \( y = x + 5 \):
\[ y = 0 + 5 = 5 \]
So the point of intersection is \( (0, 5) \).
Since there is one unique solution to this system of equations, the answer is:
1