Question

Solve by the method of elimination

3(2x + y) = 7xy, 3(x + 3y) = 11xy

Answer 1

3(2x + y) = 7xy

6x + 3y = 7xy

Divided by xy

`(6x)/(xy) + (3y)/(xy) = (7xy)/(xy)`

`6/y + 3/x` = 7

Let `1/x` = a, `1/y` = b

3a + 6b = 7 → (1)

3(x + 3y) = 11xy

3x + 9y = 11xy

Divided by xy

`(3x)/(xy) + (9y)/(xy) = (11xy)/(xy)`

`3/y + 9/x` = 11

Let `1/x` = a, `1/y` = b

9a + 3b = 11 → (2)

(1) × 3 ⇒ 9a + 18b = 21 → (3)

(2) × 1 ⇒ 9a + 3b = −11 → (2)

(3) – (2) ⇒ 15b = 10

b = `10/15 = 2/3`

Substitute the value of b = `2/3` in (1)

`3"a" + 6 xx 2/3` = 7

3a + 4 = 7

3a = 7 – 4

3a = 3

a = `3/3`

= 1

But `1/x` = a

`1/x` = 1

x = 1

But `1/y` = b

`1/y = 2/3`

2y = 3

y = `3/2`

∴ The value of x = 1 and y = `3/2`