Please help and explain?

The three numbers are -8, 19, and 40
51 = a + b +c let a, b, and c be the three numbers where a < b < c
48 = c - a
11 = a + b
51 - 11 = (a + b + c) - (a + b) = c
40 = c, c is the largest number
48 = 40 - a
8 = - a
a = - 8
11 = a +b
19 = b

LET the numbers be a , b and c

LET a be the biggest and c the smallest.

a + b + c = 51

b+c = 11

SUBTRACT a = 40

a-c = 48

40 -c = 48

c = -8

ANSWER 40. 19 , -8

Numbers: x, y, and z
1) x - z = 48
2) x + y = 11
3) x + y + z = 51 (Substitute (x + y) by 11, 2nd equation)
11 + z = 51 (Subtract 11 from both sides)
z = 40
1st) x - z = 48 (Substitute z by 40)
x - 40 = 48 (Add 40 to both sides)
x = 88
2) x + y = 11 (Substitute x by 88)
88 + y = 11 (Subtract 88 from both sides)
y = - 77
Answer: x = 88, y = -77, z = 40

Let a,b,c be the three numbers and a<b<c
then the sum of three numbers =a+b+c=51 ........(i)
the difference of largest and the smallest number=c-a=48............(ii)
the sum of two smaller numbers =a+b=11..........(iii)

From (ii) and (iii) by addition, we get
c+b=59
Put the value of c+b in (i)
=>a+59=51
=>a=-8
So we have found the least number
Now put a=-8 in (iii)
=>-8+b=11
=>b=19
The middle number has been found.
Now put b-=19, a=-8 in (i)
=>-8+19+c=51
=>11+c=51
=>c=40
So we have found the largest number.

Hence the smallest number is -8
the middle number is 19
the largest number is 40

a, b,c are largest to smallest
a+b+c = 51...[1]
a - c = 48 ....[2]
b+c = 11 ... [3]
These are based on the statements above
add equations [2] and [3[
so a+b = 59
Substitute for a+b in [1]
==> 59 + c = 51
==> c = -8
using [2] and substituting for c
a -(-8) = 48
==> a = 40
using [3]
b - 8 = 11
==> b = 19
Now, check in [1]
lhs = 40 + 19 - 8 = 51 = rhs
so the values are correct.

a+b+c=51
a-c=48
b+c=11
solve for a,b,c