These are nine equations. Is each line a separate system?Originally Posted byPanaboy

Here's how you can solve e.g. the first one:

x -4y = 6 2x+y-2z=-17 5x-y-2z=1

Solve the first equation for x:x = 6+4y

Substitute into the other two:

2(6+4y) + y -2z = 17 5(6+4y) - y - 2z = 1

and simplify:

12 + 8y + y -2z = 17 30 +20y - y -2z = 1

which becomes

9y - 2z = 5 19y - 2z = -29

Solve the first of these for 2z (since this also appears in the second equation):

2z = 9y - 5

Substitute into the second one:

19y - (9y - 5) = -29

which becomes

10y + 5 = -29

Solve this for y, then use the bold equations to find z and x, and you are done.