Question

if 3p=4q and 9q=8q-12, find the vaue of pq

Answer 1

Method 1. Substitution method

The given equations are

3p = 4q .....(1)

9p = 8q - 12 .....(2)

From (2), we get

3 (3p) = 8q - 12

or, 3 (4q) = 8q - 12 [ by (1) ]

or, 12q = 8q - 12

or, 4q = - 12

or, q = - 3

Putting q = - 3 in (1), we get

3p = 4 (- 3)

or, p = - 4

Hence, pq = (- 4) × (- 3) = 12.

Method 2. Elimination method

The given equations are

3p = 4q .....(1)

9p = 8q - 12 .....(2)

Multiplying (1) by 3, we get

9p = 12q

9p = 8q - 12

On subtraction, we have

0 = 4q + 12

or, q = - 3

Putting q = - 3 in (1), we have

3p = 4 (- 3)

or, p = - 4

Hence pq = (- 4) × (- 3) = 12.

Answer 2

Given:

3p = 4q and 9q = 8q - 12

To find:

Find the vaue of pq.

Solution:

From given, we have,

3p = 4q  ..........(1)

9q = 8q - 12  ........(2)

solving equation (2) we get,

9q = 8q - 12

9q - 8q = - 12

∴ q = - 12

in order to find the value of p, we need to use the value of q in equation (1),  

so, we get,

3p = 4q

p = 4/3 × q

= 4/3 × -12

∴ p = - 16

Now, we need to find the product pq,

pq = -16 × -12

∴ pq = 192