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

a. 20

b. 18

c. 11

d. 10

e. 5

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.