67x - 58y = 192

58x - 67y = 183

Given,

Equations :

67x - 58y = 192 ……..(1)

58x - 67y = 183 ……..(2)

Multiplying equation (1) by 58, we get :

⇒ 58(67x - 58y) = 192 × 58

⇒ 3886x - 3364y = 11136 ……..(3)

Multiplying equation (2) by 67, we get :

⇒ 67(58x - 67y) = 183 × 67

⇒ 3886x - 4489y = 12261 ………(4)

Subtracting equation (3) from (4), we get :

⇒ 3886x - 4489y - (3886x - 3364y) = 12261 - 11136

⇒ 3886x - 3886x - 4489y + 3364y = 1125

⇒ -1125y = 1125

⇒ y = $-\dfrac{1125}{1125}$ = -1.

Substituting value of y in equation (1), we get :

⇒ 67x - 58(-1) = 192

⇒ 67x + 58 = 192

⇒ 67x = 192 - 58

⇒ 67x = 134

⇒ x = $\dfrac{134}{67}$ = 2.

Hence, x = 2 and y = -1.