Given the functions f(x)=ax+b and g(x)=(1+a)x-b and (1,-2), the point of intersection of f and g lines, calculate a and b?

Since the given point is the intercepting point of the
graphs of the given functions, it's coordinates verify the expressions of the
functions.

(1, - 2) belongs to f(x)'s graph if and only
if;

f(1) = -2

f(1) = a +
b

a + b = -2 (1)

(1, - 2)
belongs to g(x)'s graph if and only if:

g(1) =
-2

g(1)=(1+a)-b

1 + a - b =
-2

a - b = -3 (2)

We'll add
(1) + (2):

a + b + a - b = -2 -
3

We'll eliminate and combine like
terms:

2a = -5

a
= -5/2

We'll substitute a in
(2):

a - b = -3

-5/2 - b =
-3

b = 3 - 5/2

b
= 1/2

The function f(x) is determined and
it's expression is:

f(x) = -5x/2 +
1/2

The function g(x) is determined and it's
expression is:

g(x) = (1 - 5/2)x +
1/2

g(x) = -3x/2 +
1/2