Question

Solve the following system of equations:

21x + 47y = 110

47x + 21y = 162

Answer 1

Given: 21x + 47y = 110; 47x + 21y = 162.

Step-wise calculation:

1. Add the two equations:

(21x + 47x) + (47y + 21y) = 110 + 162 

68x + 68y = 272

⇒ x + y = 4

2. Subtract the first equation from the second:

(47x – 21x) + (21y – 47y) = 162 – 110 

26x – 26y = 52

⇒ x – y = 2

3. Solve the two simpler equations:

Add x + y = 4 and x – y = 2

⇒ 2x = 6

⇒ x = 3

Substitute x = 3 into x + y = 4

⇒ y = 1

The solution is x = 3, y = 1 (ordered pair (3, 1)).