Question

Solve for x and y:

`x/2 - y/9 = 6, x/7 + y/3 = 5`

Answer 1

Given: `x/2 - y/9 = 6, x/7 + y/3 = 5`

Step-wise calculation:

1. Clear denominators:

Multiply the first equation by 18:

`18 xx (x/2) - 18 xx (y/9) = 18 xx 6` 

⇒ 9x – 2y = 108

Multiply the second equation by 21:

`21 xx (x/7) + 21 xx (y/3) = 21 xx 5` 

⇒ 3x + 7y = 105

2. Eliminate x:

Multiply 3x + 7y = 105 by 3

⇒ 9x + 21y = 315

Subtract 9x – 2y = 108 from 9x + 21y = 315:

(9x + 21y) – (9x – 2y) = 315 – 108

⇒ 23y = 207

⇒ `y = 207/23` 

⇒ y = 9

3. Substitute y = 9 into 3x + 7y = 105:

3x + 7(9) = 105

⇒ 3x + 63 = 105

⇒ 3x = 42

⇒ x = 14