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Easy

Question

# 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.

Hint:

### 1. For Equations with Unique solution (One solution):-

(a1/a2) ≠ (b1/b2)

2. For Equations with Infinitely Many solutions:-

(a1/a2) = (b1/b2) = (c1/c2)

3. For Equations with No solution:-

(a1/a2) = (b1/b2) ≠ (c1/c2)

## 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.

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