Question

Solve the following system of equations:

152x – 378y = –74

–378x + 152y = –604

Answer 1

Given: 152x – 378y = –74 and –378x + 152y = –604. 

Step-wise calculation:

1. Add the two equations:

(152 + (–378))x + ((–378) + 152)y = (–74 + (–604))

⇒ (–226)x + (–226)y = –678 

⇒ –226(x + y) = –678 

⇒ x + y = 3

2. Subtract the second equation from the first:

(152 – (–378))x + (–378 – 152)y = (–74 – (–604))

⇒ 530x – 530y = 530

⇒ 530(x – y) = 530 

⇒ x – y = 1

3. Solve the two simpler equations:

Add: (x + y) + (x – y) = 3 + 1

⇒ 2x = 4

⇒ x = 2

Subtract: (x + y) – (x – y) = 3 – 1

⇒ 2y = 2

⇒ y = 1

The solution is x = 2, y = 1.