Step-by-step explanation:
The given system of equations are:
2x - 3y = - 19 ............... (1)
and 4x + 5y = 17 ............... (2)
Multiplying (1) by 5 and (2) by 3, we get
5(2x - 3y) = 5(- 19)
⇒ 10x - 15y = - 95 ............... (3)
and 3(4x + 5y) = 3(17)
12x + 15y = 51 ............... (4)
Adding (3) and (4), we get
10x - 15y + 12x + 15y = - 95 + 51
⇒ 22x = - 44
⇒ x = - 2
Put x = - 2 in equation (1), we get
2(- 2) - 3y = - 19
⇒ - 4 - 3y = - 19
⇒ 3y = - 4 + 19 = 15
⇒ y = 5
∴ x = - 2 and y = 5
Thus, the "required option C) (- 2, 5)" is correct.
