The functions g and h are such that
g(x) = 2x + 5
and
h(x) = ax + b
where a and b are constants.
h(3) = 26
and g (21) = h(1)
Find the value of a and the value of b.

a = - 10.5, b = 57.5

Step-by-step explanation:

Evaluate h(3) by substituting x = 3 into h(x)

h(3) = 3a + b = 26 → (1)

g(21) = 2(21) + 5 = 42 + 5 = 47

h(1) = a + b, thus

3a + b = 26 → (1)

a + b = 47 → (2)

Subtract (2) from (1) term by term to eliminate the term in b

2a = - 21 ( divide both sides by 2 )

a = - 10.5

Substitute a = - 10.5 into either of the 2 equations for value of b

Substituting in (2)

- 10.5 + b = 47 ( add 10.5 to both sides )

b = 57.5