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9 November, 10:41

3x + y = 19 and x + 3y = 1. Find the value of 2x + 2y.

a. 20

b. 18

c. 11

d. 10

e. 5

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Answers (1)
  1. 9 November, 12:41
    0
    2x + 2y = 10

    (d) is the correct option.

    Step-by-step explanation:

    The given set of equations are 3x + y = 19 and x + 3y = 1

    Now, Let us try and find the values of x and y from these equation.

    3x + y = 19 ... (1)

    x + 3y = 1 ... (2)

    Multiple equation (2) by 3 and subtract from (1), we get

    3x + y - 3 (x + 3y) = 19 - 3 (1)

    or, 3x + y - 3x - 9y = 19 - 3

    or, - 8y = 16

    or, y = 16/-2 = - 2

    So, y = - 2

    Put this value in (1), we get

    3x - 2 = 19

    or, 3x = 19 + 2 = 21 ⇒ x = 21/3 = 7

    So, x = 7 and y = - 2 is the solution of the given set of equations.

    So, 2x + 2y = 2 (7) + 2 (-2) = 14 - 4 = 10

    ⇒ 2x + 2y = 10

    (d) is the correct option.
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