Solve the following system

Question

2x  +z=4

 

2x-y   =4

 

 x+y-z=0

Answer 1

2x+z=4

2x-y=4

x+y-z=0

from equation 1 we get z=4-2x

substitute into equation 3

x+y-(4-2x)=0

x+y-4+2x=0

3x+y-4=0

3x+y=4  and now use this equation and equation 2

2x-y=4

add

5x=8

x=8/5

use equation 2

2(8/5)-y=4

16/5-y=4

-y=4-16/5

-y=4/5

y=-4/5

now use equation 3

x+y-z=0

x+y=z

(8/5)+(-4/5)=z

4/5=z

(8/5,  -4/5,  4/5) is the solution