Question

Solve: 23x + 29y = 98, 29x + 23y = 110.

Answer 1

Given: 23x + 29y = 98, 29x + 23y = 110.

Step-wise calculation:

1. Add the two equations:

(23x + 29y) + (29x + 23y) = 98 + 110 

⇒ 52x + 52y = 208

⇒ x + y = 4

2. Subtract the first equation from the second:

(29x + 23y) – (23x + 29y) = 110 – 98 

⇒ 6x – 6y = 12

⇒ x – y = 2

3. Solve the system x + y = 4 and x – y = 2:

Add: 2x = 6

⇒ x = 3 

Then y = 4 – x

= 1