An algebraic expression of the form a + bx has the value of 15 when x = 2 and the value of 3 when x = 5. Calculate a + b.

The value of the expression (a + b) = 19

Step-by-step explanation:

The given expression is a + bx.

Case - I when x = 2, (a + bx) = 15

Putting the value of x, we get: a + 2b = 15

or, a = 15 - 2b ... (1)

CAse II - when x = 5, (a + bx) = 3

Putting the value of x, we get a + 5b = 3

or a = 3 - 5b ... (2)

Comparing (1) and (2)

15 - 2b = 3 - 5b

or, 5b - 2b = 3 - 15

or, 3b = - 12 ⇒ b = - 4

if b = - 4, then a = 3 - 5b = 3 + 20 = 23

Hence, a = 23, b = - 4

So, the value of (a + b) = 23 - 4 = 19