prealgebra

[bwilloughby2010]

I need help on how to solve this equation because I dont understand how to start or the steps to solve it.

Linear Equations

-2x -y +z = 5
x +3y -2z =12
2x -4y +z =0

thanks
Beatrice

 

[masters]

I need help on how to solve this equation because I dont understand how to start or the steps to solve it.

Linear Equations

-2x -y +z = 5
x +3y -2z =12
2x -4y +z =0

thanks
Beatrice

Hi bwilloughby2010,

There are several methods to solve this system. I don't know what you've been taught, but since you are unsure of how to start, I'll demonstrate the "elimination" method. You can "google" this method if you haven't used it before.

[1] \(\displaystyle -2x-y+z=5\)

[2]\(\displaystyle x+3y-2z=12\)

[3] \(\displaystyle 2x-4y+z=0\)

The idea here is to take two of the equations, manipulate one or both to get the coefficients of one of the variables to be the additive inverses of each other. Then, when we add them together, they are eliminated.

Add [1] + [3]

[1] \(\displaystyle -2x-y+z=5\)
[3] \(\displaystyle 2x-4y+z=0\)
--------------------------------
[4] \(\displaystyle -5y+2z=5\)

Next, multiply [2] by 2 and add to [1]

[1] \(\displaystyle -2x-y+z=5\)
[2] \(\displaystyle 2x+6y-4z=24\)
---------------------------------
[5] \(\displaystyle 5y-3z=29\)

Now, use [4] and [5], and the same method of elimination to solve for y and z. After that, x can be easily found.

Show us how you made out.