Final answer:
To find which system(s) have point a as their intersection, we solve each pair of equations. None of the provided systems have the same intersection point unless point a is defined explicitly, in which case we could identify the corresponding system.
Step-by-step explanation:
To identify the systems of equations that have the same point of intersection, we look for a common solution to each system. The common solution is the point a where their graphs would intersect on a coordinate plane.
System a: Y = X - 4 and Y = 5X - 7
To find the intersection, set the two equations equal to each other: X - 4 = 5X - 7. Solve for X, which gives us X = 1, and subsequently Y = -3. Thus, point a for the first system is (1, -3).
System b: Y = 3X - 10 and Y = X - 1
Set the equations equal: 3X - 10 = X - 1. Solving for X, we get X = 4.5, and for Y, we get -1.5. So, point a is (4.5, -1.5).
System c: Y = 2X - 7 and Y = 5X - 16
Equalize and solve the equations: 2X - 7 = 5X - 16. We find X = 3 and Y = -1, which gives the intersection point a as (3, -1).
Each system has its own unique intersection point, which means if a refers to a specific point, we would need that specific point to determine which system or systems have a as their point of intersection.