Solve 2x + y = 23, 4x - y = 19. Hence, find the values of x - 3y and 5y - 2x.

Given,

2x + y = 23 …….(i)

4x - y = 19 …….(ii)

Multiplying eq. (i) by 2 we get,

4x + 2y = 46 ……(iii)

Subtracting eq. (ii) from (iii) we get,

⇒ 4x + 2y - (4x - y) = 46 - 19

⇒ 4x - 4x + 2y + y = 27

⇒ 3y = 27

⇒ y = 9.

Substituting value of y in eq. (ii) we get,

⇒ 4x - 9 = 19

⇒ 4x = 28

⇒ x = 7.

Substituting value of x and y in x - 3y,

⇒ x - 3y = 7 - 3(9) = 7 - 27 = -20.

Substituting value of x and y in 5y - 2x,

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

Hence, x = 7, y = 9, x - 3y = -20 and 5y - 2x = 31.