If 2x + y = 23 and 4x - y = 19; find the values of x - 3y and 5y - 2x.

Given,

Equations : 2x + y = 23 and 4x - y = 19

⇒ 2x + y = 23

⇒ y = 23 - 2x …….(1)

Substituting value of y from equation (1) in 4x - y = 19, we get :

⇒ 4x - (23 - 2x) = 19

⇒ 4x - 23 + 2x = 19

⇒ 6x = 19 + 23

⇒ 6x = 42

⇒ x = $\dfrac{42}{6}$ = 7.

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

⇒ y = 23 - 2(7) = 23 - 14 = 9.

⇒ x - 3y = 7 - 3 × 9 = 7 - 27 = -20

⇒ 5y - 2x = 5 × 9 - 2 × 7 = 45 - 14 = 31.

Hence, x - 3y = -20 and 5y - 2x = 31.