Question

Solve for x and y:

`x/3 + y/4 = 11, (5x)/6 - y/3 = -7`

Answer 1

Given: `x/3 + y/4 = 11, (5x)/6 - y/3 = -7`

Step-wise calculation:

1. Clear denominators:

Multiply first equation by 12:

`12 xx (x/3 + y/4) = 12 xx 11` 

⇒ 4x + 3y = 132

Multiply second equation by 6:

`6 xx ((5x)/6 - y/3) = 6 xx (-7)` 

⇒ 5x – 2y = –42

2. Now use elimination (standard elimination method).

Multiply 4x + 3y = 132 by 2

⇒ 8x + 6y = 264

Multiply 5x – 2y = –42 by 3 

⇒ 15x – 6y = –126

Add the two results:

(8x + 15x) + (6y – 6y) = 264 + (–126) 

⇒ 23x = 138

⇒ `x = 138/23`

⇒ x = 6

3. Substitute x = 6 into 5x – 2y = –42:

5(6) – 2y = –42 

⇒ 30 – 2y = –42 

⇒ –2y = –72 

⇒ y = 36