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

13x + 11y = 70

11x + 13y = 74

Given, equations :

⇒ 13x + 11y = 70 ……….(1)

⇒ 11x + 13y = 74 ……….(2)

Multiplying equation (1) by 11, we get :

⇒ 11(13x + 11y) = 11 × 70

⇒ 143x + 121y = 770 ……..(3)

Multiplying equation (2) by 13, we get :

⇒ 13(11x + 13y) = 13 × 74

⇒ 143x + 169y = 962 ……..(4)

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

⇒ 143x + 169y - (143x + 121y) = 962 - 770

⇒ 143x - 143x + 169y - 121y = 192

⇒ 48y = 192

⇒ y = $\dfrac{192}{48}$ = 4

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

⇒ 13x + 11(4) = 70

⇒ 13x + 44 = 70

⇒ 13x = 70 - 44

⇒ 13x = 26

⇒ x = $\dfrac{26}{13}$ = 2.

Hence, x = 2 and y = 4.