SOLUTION: I need help solving this problem using the Gaussian Elimination method step by step please! 4x+3y+2z=6 -2x-y+5z=5 x+2y-3z=3 thank you in advance!

Question 148619: I need help solving this problem using the Gaussian Elimination method step by step please!
4x+3y+2z=6
-2x-y+5z=5
x+2y-3z=3
thank you in advance!

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1.
2.
3.
Combine equations to remove one of the variables.
Multiply eq. 2 by (3) and add to eq. 1,
2.
2.
This gets rid of y and makes a new eq. 1 with just x and z,
1.
1.
Multiply eq. 2 by (2) and add to eq. 3,
2.
2.
This gets rid of y and makes a new eq. 3 with just x and z,
3.
3.
Now we have two equations in x and z.
1.
3.
We can continue to reduce to one variable.
Multiply eq. 1 by 3 and eq. 3 by -2 and add them to get rid of x,
1.
1.
3.
3.
Now add the two eqs.

Now that you have z, work backwards and back substitute to find x and then y.
You can use any of the previous equations to solve for other variables.

And finally for y,
2.

(x,y,z)=(-2,4,1)
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