I need help solving these equations:

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

2y +3z=1 x-3y+z=10 3x+4y+z=-2

2x -z= 3 x+4y-2z=-23 2x+5y-z=-11

system of equation with three varialbles

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- Oct 31st 2005, 03:21 PMPanaboyhomework help please
I need help solving these equations:

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

2y +3z=1 x-3y+z=10 3x+4y+z=-2

2x -z= 3 x+4y-2z=-23 2x+5y-z=-11

system of equation with three varialbles - Oct 31st 2005, 05:52 PMhpeQuote:

Originally Posted by**Panaboy**

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.