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)

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.

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europa2433

europa2433

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