Thread: system of equations

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

Originally Posted by Panaboy

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

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

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.