For solving each pair of equations, use the method of elimination by equating coefficients :

41x + 53y = 135

53x + 41y = 147

Given, equations :

⇒ 41x + 53y = 135 ………(1)

⇒ 53x + 41y = 147 ………(2)

Multiplying equation (1) by 53, we get :

⇒ 53(41x + 53y) = 53 × 135

⇒ 2173x + 2809y = 7155 …….(3)

Multiplying equation (2) by 41, we get :

⇒ 41(53x + 41y) = 41 × 147

⇒ 2173x + 1681y = 6027 …….(4)

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

⇒ 2173x + 2809y - (2173x + 1681y) = 7155 - 6027

⇒ 2173x - 2173x + 2809y - 1681y = 1128

⇒ 1128y = 1128

⇒ y = $\dfrac{1128}{1128}$ = 1.

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

⇒ 41x + 53y = 135

⇒ 41x + 53(1) = 135

⇒ 41x + 53 = 135

⇒ 41x = 135 - 53

⇒ 41x = 82

⇒ x = $\dfrac{82}{41}$ = 2.

Hence, x = 2 and y = 1.