Does the following system of equations have a solution? if so, find one. if not, explain why not. 2x+y+z=4, x-y+3z=-2, -x+y+z=-2.

x=2, y=1, z=-1

Step-by-step explanation:

Given

2x+y+z=41

x-y+3z=-22

-x+y+z=-23

Add 2 & 3 we get

4z=-4

z=-1

Put value of z in 1 & 2

2x+y-1=4

2x+y=53

x-y+3(-1)=-2

x-y=14

add 3 & 4 we get

x=2

Put x & z in 1

y=1