SOLUTION: x+y+z=30000 .02x+.03y+.06z=1110 .02x+150=.03y : solve for x,y, and z. The problem im having with this problem is the "z" variable. It is only on 2 of the 3 equations. Iv

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: x+y+z=30000 .02x+.03y+.06z=1110 .02x+150=.03y : solve for x,y, and z. The problem im having with this problem is the "z" variable. It is only on 2 of the 3 equations. Iv      Log On


   

Question 106811: x+y+z=30000
.02x+.03y+.06z=1110
.02x+150=.03y : solve for x,y, and z.
The problem im having with this problem is the "z" variable. It is only on 2 of the 3 equations. Ive been trying to solve by using the method of elimination, but I cant seem to isolate the variables. thank you.

Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Elimination method is perfect for this system!

First let's eliminate x! To do that, let's use x%2By%2Bz=30000 and .02x%2B.03y%2B.06z=1110+.
Let's multiply x%2By%2Bz=30000 by 2!

2x%2B2y%2B2z=60000
Now, let's multiply 0.02x%2B0.03y%2B0.06z=1110+ by 100!
2x%2B3y%2B6z=111000

It's elimination time!

Line up the equations
_____________________________2x+3y+6z=111000
_____________________________2x+2y+2z=60000

If you subtract
2x%2B2y%2B2z=60000 from 2x%2B3y%2B6z=111000,
you'll get
y%2B4z=51000
Solving y%2B4z=51000.
y=-4z%2B51000

Now, let's eliminate y! we'll do that by using 0.02x%2B0.03y%2B0.06z=1110+ and
0.02x%2B150=0.03y
Solving 0.02x%2B150=0.03y,
0.02x-0.03y=-150
Multiplying this by 100,
2x-3y=-15000
Multiplying .02x%2B.03y%2B.06z=1110+ by 100,

2x%2B3y%2B6z=111000

it's elimination time!

Line up the equations!

______________________________2x+3y+6z=111000
______________________________2x-3y =-15000
If you add these, you'll get:
4x%2B6z=96000
Solving this,
4x=-6z%2B96000
x=-3z%2F2%2B24000
Substituting x=-3z%2F2%2B24000 and y=-4z%2B51000 to 2x-3y=-15000,
2%28-3z%2F2%2B24000%29-3%28-4z%2B51000%29=-15000
-3z%2B48000-%28-12z%2B153000%29=-15000
-3z%2B48000%2B12z-153000=-15000
%28-3z%2B12z%29%2B%2848000-153000%29=-15000
9z-105000=-15000
9z=-15000%2B105000
9z=90000
z=10000
Yahoo! we found the value of z at last!
But wait, there's more!
Remember that x=-3z%2F2%2B24000. So,
x=-3%2810000%29%2F2%2B24000
x=-30000%2F2%2B24000
x=-15000%2B24000
x=13000

Also,
y=-4z%2B51000. So,
y=-4%2810000%29%2B51000
y=-40000%2B51000=11000

therefore, x=13000, y=11000, and z=10000.

Power up,
HyperBrain!