Question

In the solution to this system, what is the value of y? x+y+z=1x+y+z=1 2x+y−z=82x+y-z=8 x−y+z=−5

Answer 1

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