Which ordered pair is the solution for the system? 2x - 3y = - 19 4x + 5y = 17 A) (2, 1) B) (2, 5) C) (-2, 5) D) (-1, 3)

The "required option C) ( - 2, 5) " is correct.

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.