He sum of three numbers is 19 . the sum of twice the first number, 4 times the second number, and 5 times the third number is 72 . the difference between 4 times the first number and the second number is 12 . find the three numbers ti84

Let 
x> the first number
y> the second number
z> the third number

we know that
x+y+z=19> z=19-x-y> equation 1
2x+4y+5z=72> equation 2
4x-y=12> equation 3

substitute equation 1 in 2
2x+4y+5*[19-x-y]=72> 2x+4y+95-5x-5y=72> -3x-y=-23
3x+y=23> equation 4

add equation 3 and equation 4
4x-y=12
3x+y=23

7x+0y=35> x=35/7> x=5
4x-y=12> y=4x-12> y=4*5-12> y=8
z=19-x-y> z=19-5-8> z=6

the answer is
the numbers are
5 
8
6