Eliminate the “z” variable in the last two equations by finding opposite coefficients and adding. What is the resulting equation?

x + 3y + 2z = –16
2x – y + 2z = –15
2x – 2y – z = 1

Question

Eliminate the “z” variable in the last two equations by finding opposite coefficients and adding. What is the resulting equation?

x + 3y + 2z = –16
2x – y + 2z = –15
2x – 2y – z = 1

anonymous · Answer

2x-y+2z=-15
2x-2y-z=1

2x -y + 2z= -15 
2(2x-2y-z)= 2(1)

which is 


2x -y + 2z= -15
4x-4y -2z = 2

You now add the like components of the equation (i.e. x with x, y with y, and constants with constants).
This gives you:

(2x+4x)+(-y-4y)+(2z-2z)=(-15+2)

which simplifies to:

6x-5y+0=-13