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