To determine the number of solutions to the given system of linear equations:
- y = x + 5
- y = -x + 5
Let's analyze the two equations.
First, we can set the two equations equal to each other to find any points of intersection:
\[ x + 5 = -x + 5 \]
Now, add \(x\) to both sides:
\[ x + x + 5 = 5 \]
This simplifies to:
\[ 2x + 5 = 5 \]
Next, subtract 5 from both sides:
\[ 2x = 0 \]
Now, divide both sides by 2:
\[ x = 0 \]
Now that we have \(x\), we can substitute \(x = 0\) back into either equation to find the corresponding \(y\):
Using the first equation:
\[ y = 0 + 5 = 5 \]
So the solution to the system of equations is \( (0, 5) \).
Since we found one unique solution where both lines intersect, the answer is:
1