Given the functions f(x)=ax+b-9 and g(x)=2bx-a find a and b if the point A(2,3) is on the graphs of f and g.

Since the point A is located on both graphs, then its
coordinates verify the equations of the functions f and
g.

f(2) = 3

f(2) = 2a + b -
9

2a + b - 9 = 3

We'll move
the numbers alone to the right side, keeping a and b to the left
side:

2a + b = 12 (1)

Also,
g(2) = 3

g(2) = 4b - a

-a + 4b
= 3 (2)

We'll mutliply (2) by
2:

-2a + 8b = 6 (3)

We'll add
(3) to (1):

2a + b - 2a + 8b = 12 +
6

We'll eliminate like
terms:

9b = 18

b =
2

a = 4b - 3

a = 8 -
3

a = 5

The
values of a and b are: a = 5 and b = 2.