The given system of linear equations is:
Y = x + 5 ...(1)
y = -x + 5 ...(2)
To determine the number of solutions, we can compare the slopes of the two equations.
The equation (1) is in the form Y = mx + b, where m is the slope. So, the slope of equation (1) is 1.
The equation (2) is also in the form y = mx + b, where m is the slope. So, the slope of equation (2) is -1.
Since the slopes of the two equations are different, this means that the lines represented by the equations are not parallel.
If two lines are not parallel, they must intersect at exactly one point. Therefore, the system of linear equations has 1 solution.
Hence, the answer is 1.