Graph each system and determine the number of solutions that it has. If it has one solution, name it. 9. \( \begin{array}{l}x-y=1 \\ x+y=5\end{array} \)

To graph the system of equations, we first rewrite each equation in slope-intercept form (y = mx + b): 1. For the first equation \( x - y = 1 \), rearranging gives \( y = x - 1 \). 2. For the second equation \( x + y = 5 \), rearranging gives \( y = -x + 5 \). Now, let's graph these two equations. The first line, \( y = x - 1 \), has a slope of 1 and a y-intercept at -1. The second line, \( y = -x + 5 \), has a slope of -1 and a y-intercept at 5. When graphed, these two lines will intersect at a point. To find the exact coordinates of the intersection (the solution), we can solve the system algebraically. Setting the equations equal to each other: \( x - 1 = -x + 5 \). Adding x to both sides: \( 2x - 1 = 5 \). Adding 1 to both sides: \( 2x = 6 \). Dividing by 2: \( x = 3 \). Substituting \( x = 3 \) into one of the original equations (let’s use \( x + y = 5 \)): \( 3 + y = 5 \). So, \( y = 2 \). The lines intersect at the point (3, 2), which is the solution to the system. Thus, there is exactly one solution, and it is (3, 2). In conclusion, this system has one solution: (3, 2).