Question

Two equations are given below:

a − 3b = 9
a = b − 3

What is the solution to the set of equations in the form (a, b)?

(−9, −6)
(−4, −3)
(−6, −3)
(−9, −7)

Answer 1

a - 3b = 9
a = 9 + 3b

therefore eq. 1 equals eq.2 (a = b -3)

b - 3 = 9 + 3b
b - 3b = 9 + 3
-2b = 12
b = -6 (Answer)


by substituting b in eq. 2

a = b - 3
a = -6 - 3
a = - 9 (Answer)


(a,b)
(-9,-6)

Answer 2

Option (a) is correct.

The solution to the set of equations in the form (a, b) is (-9 , -6)

Explanation:

Given :Two equations are

a − 3b = 9

a = b − 3

We have to find the solution to the set of equations in the form (a, b)

Consider the given system of linear equation,

a − 3b = 9 ......(1)

a = b − 3 ...........(2)

(2) can be written as a - b = - 3 .......(3)

We will solve the given system using elimination method and eliminate a ,

Subtract (3) from (1) , we have,

a − 3b -(a - b) = 9 + 3

-3b + b = 12

-2b = 12

b = - 6

Substitute b = - 6 in (2) , we have,

a = b − 3 ⇒ a = -6 - 3 = -9

Thus, the solution to the set of equations in the form (a, b) is (-9 , -6)