Question

Solve the following system of equations.

x + 4y + z = –10
3x – 3y + 6z = –21
x + 2y + 2z = –10

Answer 1

x + 4y + z = –10 . . . (eq 1)
3x – 3y + 6z = –21 . .(eq 2)
x + 2y + 2z = –10 . . (eq 3)

divide left and right of the second (eq 2) by 3

3x - 3y + 6z = -21
x - y +2z = -7

subtract this equation from the third

x + 2y + 2z = -10
x - y + 2z = -7
---------------- -
3y = -3
y = -1

enter this value in (eq 1) and (eq 3)

x + 4(-1) + z = –10
x + z = -6 . . . . . (eq 4)

x + 2(-1) + 2z = –10
x + 2z = –8 . . . . (eq 5)

subtract (eq 4) from (eq 5)

x + 2z = –8
x + z = -6
---------- -
z = -2

enter this value in (eq 4)
x -2 = -6
x = -4

Answer:
x = -4
y = -1
z = -2