x + y + z = 1 x - y + 5z = 13 5x + y + z = -19?

x+ y + z = 1 ...... [1]
x - y + 5z = 13 ...... [2]
5x + y + z = -19 ...... [3]

[1] + [2] :
2x + 6z = 14
x + 3z = 7 ...... [4]

[2] + [3] :
6x + 6z = -6
x + z = -1 ...... [5]

[4] - [5] :
2z = 8
z = 4

Put z = 4 into [5] :
x + 4 = -1
x = -5

Put x = -5 and z = 4 into [1] :
-5 + y + 4 = 1
y = 2

Hence, x = -5, y = 2, z = 4

Well,

x + y + z = 1 (1)
x - y + 5z = 13 (2)
5x + y + z = -19 (3)

(3) - (1) gives
4x = -20 ==> x = -5
therefore (1) and (2) becomes
-5 + y + z = 1 (3)
-5 - y + 5z = 13 (4)
therefore (3) + (4) gives
-10 + 6z = 14
6z = 24
z = 4

x = -5 and z = 4 and x + y + z = 1 gives
-5 + y + 4 = 1
y = 2

conclusion :
x = -5
y = 2
z = 4

hope it' ll help !!

x = -5, y = 2, z = 4

solve just like any other simultaneous equation.

rearrange first equation:

x = 1-y-z
substitute for x in the other two.

(1-y-z) - y + 5z = 13
5(1-y-z) + y + z = -19

simplify
1-2y + 4z = 13
5-4y-4z = -19

add the two
6-6y = -6
6+6 = 6y
12 = 6y
y = 2

substitute into 5-4y-4z = -19
5 - 4(2) -4z = -19
5 - 8 -4z = -19
-3 - 4z = -19
19-3 = 4z
16 = 4z
z = 4

lastly substitute into x+y+z = 1
x+2+4 = 1
x+ 6 = 1
x = 1-6
x = -5

solution (-5,2,4)