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.

18

step-by-step explanation: