Question

Solve the following pair of linear equations.

152x − 378y = − 74

− 378x + 152y = − 604

Answer 1

152x − 378y = − 74

76x − 189y = − 37

`x =(189y - 37)/76  ...(1)`

− 378x + 152y = − 604

− 189x + 76y = − 302 … (2)

Substituting the value of x in equation (2), we obtain

`-189((189y-37)/76)+76y = - 302`

− (189)² y + 189 × 37 + (76)² y = − 302 × 76

189 × 37 + 302 × 76 = (189)² y − (76)² y

6993 + 22952 = (189 − 76) (189 + 76) y

29945 = (113) (265) y

y = 1

From equation (1), we obtain

`x = (189(1)-37)/76`

`x =(189-37)/76 = 152/76`

x = 2