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