Algebra 2 question?

Question

Please solve the system:

x - 4y - 5z = -22
2x - 2y + 5z = -11
4x + 3y + z = -10

Answer 1

x - 4y - 5z = -22
2x - 2y + 5z = -11
4x + 3y + z = -10

multiply 1st eq by -2 and add to 2nd eq
Also multiply 2nd eq by -2 and add to 3rd eq
and get
6y + 15z = 33
7y - 9z = 12

For these 2 equations
Multiply 1st by 7 and 2nd by -6 and add
and get
159z = 159
z = 1

6y + 15z = 33
6y + 15(1) = 33
6y = 18
y = 3

x - 4y - 5z = -22
x - 4(3) - 5(1) = -22
x - 12 - 5 = -22
x = -5

Solution (-5, 3, 1)

Answer 2

x - 4y - 5z = -22
2x - 2y + 5z = -11 * -1
4x + 3y + z = -10
=>
x - 4y - 5z = -22
-2x + 2y + 5z =11
4x + 3y + z = -10
=>
x - 4y - 5z = -22 +
-2x + 2y + 5z =11
=
-x -2y = -11

Do the same method with the second and third equations.

-19x - 19y = -38
=>
x + y = -2
combine x + y = -2 and -x -2y = -11 to get y = 13 and x = -15
then you substitute x and y in one of the first equations to get z = -3

Answer 3

Add equations 1 and 2 getting:
3x-6y =-33 Eq 4
Add equation to 5 times equation 3 getting
21x +11y = -72 Eq5
Add Eq 5 to -7 times Eq 4 getting
53y = 159
y = 3
21x +11(3) = -72
21x = -105
x = -5
-5 -4(3) -5z= -22
-5z = -5
z = 1

Answer 4

x - 4y - 5z = - 22
20x + 15y + 5z = - 50-----ADD

21x + 11y = - 72

x - 4y - 5z = - 22
2x - 2y + 5z = - 11-----ADD

3x - 6y = - 33

3x - 6y = - 33
21x + 11y = - 72

- 21x + 42y = 231
21x + 11y = - 72------ADD

53y = 159
y = 3

3x - 18 = - 33
3x = - 15

x = - 5

- 5 - 12 - 5z = - 22
5 + 12 + 5z = 22------ADD

5z = 5
z = 1

x = - 5 , y = 3 , z = 1

Answer 5

x = -5
y = 3
z =1 . . . .