I just need to find the answer

Question

A function is given as f(x)=ax+b

It is known that f(1)=6 and f(2)=10

Work out the value of ab

Answer 1

GIVEN: f(x) = ax + b , f(1) = 6 and f(2)=10.

SOLUTION: f (1) = 6 ------------> A

f (x) = a x + b ----------->B

substitute x=1, we get f (1) = a(1)+b

6 = a + b [from equation ----->A, f(1)=6]

So, a + b = 6 ---------->1

f (1) = 6 ------------> C

f (x) = a x + b ----------->D

substitute x=2, we get f (2) = a(2)+b

10 = 2a + b [from equation ----->C, f(2)=10]

So, 2a + b = 10 ---------->2

Now, solving equations ----> 1 and 2, we get

a + b = 6 ------------->1

2a + b = 10 ------------>2

_-__-___-____ [By subtracting equation 1 from 2]

- a +0 = - 4

a = 4 -----------> 3

substitute equation 3 in -------->1

we get, a + b = 6

4 + b = 6

b = 6 - 4

b = 2

ANSWER :- Hence, a = 4 and b = 2

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