The Weight of Abhi’s dog can be found using the expression 2(x+3), where x is the number of weeks. The weight of tarun’s dog can be found using the expression3(x + 1), where x is the number. Will the dogs ever be the same weight ? explain.

The correct answer is: 2 (6x + 9 - 3x) = 5x + 21 can be classified as an equation with only one solution.

Step-by-step solution:-
Let y be the weight of dogs.
From the given information, we get-
Weight of Abhi's dog = 2 (x + 3)
∴ y = 2 (x + 3)
∴ y = 2x + 6
∴ -6 = 2x - y
i.e. 2x - y = -6 …................................................... (Equation i)
Weight of Tarun's dog = 3 (x + 1)
∴ y = 3 (x + 1)
∴ y = 3x + 3
∴ -3 = 3x - y
i.e. 3x - y = -3 …................................................... (Equation ii)
We need to find whether the weights of their dogs would ever be the same.
i.e. we need to solve the 2 equations and check whether the given set of simultaneous equations have a solution or not.
Now, comparing Equations i & ii with the standard form of Equations i.e. ax + by = c, we get-
a1 = 2, b1 = -1, c1 = -6
a2 = 3, b2 = -1, c2 = -3
We check the following-
a1/a2 = 2/3
b1/b2 = -1/-1 = 1
c1/c2 = -6/-3 = 2
We observe that for the above simultaneous equations,
a1/a2 ≠ b1/b2
∴ the given set of equations have only 1 solution.
Step-by-step solution:-
Simplifying the given equation i.e. 2(6x + 9 - 3x)= 5x + 21, we get-
2(6x + 9 - 3x) = 5x + 21
∴ 12x + 18 - 6x = 5x + 21 ................................. (Opening the bracket and multiplying the number with entire expression on LHS)
∴ 12x - 6x - 5x = 21 - 18 .................................. (Taking variables and constants on either side of the equation)
∴ x = 3
Since after simplifying the given equation, we get a single value of x i.e. 3 that will satisfy the given equation, we can conclude that the given equation has 1 solution.
Final Answer:-
∴ The given equation i.e. 2 (6x + 9 - 3x) = 5x + 21 can be classified as an equation with only one solution.