SOLUTION: Solve the following system of equations. x + 3y + 2z = –16 2x – y + 2z = –15 2x – 2y – z = 1

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the following system of equations. x + 3y + 2z = –16 2x – y + 2z = –15 2x – 2y – z = 1       Log On


   

Question 530260: Solve the following system of equations.
x + 3y + 2z = –16
2x – y + 2z = –15
2x – 2y – z = 1
Answer by Math_prodigy(24) About Me  (Show Source):
You can put this solution on YOUR website!
x + 3y + 2z = –16 (a)
2x – y + 2z = –15 (b)
2x – 2y – z = 1 (c)
Eliminate z:
a-b: -x+4y=-1
2c: 4x-4y-2z=2
b+2c: 6x-5y=-13
We got new system
-x+4y=-1
6x-5y=-13
Solve it:
x=4y+1
6(4y+1)-5y=-13
24y+6-5y=-13
19y=-19
y=-1
x=4*(-1)+1=-3
Substitute x and y into (c)
z=2x-2y-1=2*(-3)-2*(-1)-1
z=-5
ans: -3, -1, -5