In the solution to this system, what is the value of y?

x+y+z=1 x+y+z=1

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

x-y+z=-5

If you have multiple equations with multiple variables, you can either do clever substitutions, or turn it into a matrix on which you can perform linear combinations or multiplications (Gauss elimination)

1 1 1 1

2 1 - 1 8

1 - 1 1 - 5

(note how the above 3 rows represent the 3 equations, just got rid of the variables, plus sign and equals sign)

subtract row1 from row3, that eliminates x and z from row 3.

1 1 1 1

2 1 - 1 8

0 - 2 0 - 6

divide row3 by - 2, that will give y a factor of 1

1 1 1 1

2 1 - 1 8

0 1 0 3

The last row now says y=3