Question

Here is an identity.
a(4x – 10) = 24x + 5b
Work out the values of a and b

Answer 1

The value of a is 6 and the value of b is -12

Explanation:

Given identity is:

a(4x – 10) = 24x + 5b

We can use the comparison of coefficients method to find the values of a and b

So,

By simplifying the left hand side of identity

`4ax-10a = 24x+5b\\4ax+(-10)a = 24x+5b`

Comparing the co-efficient of x

`4a = 24\\a = (24)/(4)\\a = 6`

Comparing the constant terms

`-10a = 5b`

Putting the value of a

`-10(6) = 5b\\-60 = 5b\\b = (-60)/(5)\\b = -12`

Hence,

The value of a is 6 and the value of b is -12