If 3x + 7y = 78 and x + 3y = 32, then 2x + y = ? 

Given:

3x + 7y = 78 ...(1)

x + 3y = 32 ...(2)

Formula used:

Solving simultaneous equations.

Calculation:

Multiply equation (2) by 3:

3(x + 3y) = 3(32)

3x + 9y = 96 ...(3)

Subtract equation (1) from equation (3):

(3x + 9y) - (3x + 7y) = 96 - 78

2y = 18

y = 18 / 2

y = 9

Substitute y = 9 in equation (2):

x + 3(9) = 32

x + 27 = 32

x = 32 - 27

x = 5

Now, find 2x + y:

2x + y = 2(5) + 9

2x + y = 10 + 9

2x + y = 19

∴ 2x + y = 19.