Question 41176
x+y+z=2
2x-3y+z=-11
-x+2y-z=8

Let's add the first and the third equations. Since x's and z's in these equations have opposite coefficients, we can drop them out.

x+y+z=2
-x+2y-z=8

3y=10 (divide each side by 3)
3y/3=10/3
y=10/3

Let's plug in the value of y in the first equation.

10/3+y+z=2  (move 10/3 to the right of the equation)
x+z=2-10/3
x+z=-4/3

Now, let's plug the value of y in the second equation.
2x-3y+z=-11
2x-3.(10/3)+z=-11
2x-10+z=-11  (move -10 to the right of the equation)
2x+z=-11+10
2x+z=-1

Now we have found;

x+z=-4/3
2x+z=-1

Let's multiply the first equation by -1 to create opposite coefficients for z.

-x-z=4/3
2x+z=-1

Now let's add the two equations to drop out z;

x=1/3

When we plug the value of x in the first equation (you may plug it in the second equation as well);
-1/3-z=4/3 (move -1/3 to the right of the equation)
-z=4/3+1/3
-z=5/3     (divide each side by -1)
z=-5/3

So, y=10/3, x=1/3, z= -5/3