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13 February, 22:39

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)

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  1. 14 February, 00:23
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    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.
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