The graph shown represents the equation y=3(1/3)^x

No, it is not a solution. It makes the first equation true, but the second equation is false when (x,y) = (16, 1)

To check a possible solution, we replace the variable letters with their actual numbers. The given solution is (x,y) = (16,1) so x = 16 and y = 1 pair up. We'll replace x with 16, and replace y with 1.

Do so with the first equation and simplify

y = (-1/4)*x + 5

1 = (-1/4)*16 + 5

1 = -4 + 5

1 = 1 ... true

And repeat for the second equation

y = (1/6)*x - 2

1 = (1/6)*16 - 2

1 = 2.667 - 2

1 = 0.667 false

The equation above is false, so the original equation is false when (x,y) = (16,1). This proves the point is not on the line.

So overall, (16,1) is not a solution to the system.