Use Gaussian elimination with back substitution?

Question

Use Gaussian elimination with back substitution to solve the following system:

 

x₁+x₂+x₃=1,

x₁+2x₂+2x₃=1,

x₁+2x₂+3x₃=1.

 

The answer is (1, 0, 0) but I don't know how to get there. Please show all your work step by step. Thanks.

Answer 1

X1+x2+x3=1

x1+2x2+2x3=1

x1+2x2+3x3=1

 

Subtracting equation 3 from equation 2

 

-x3=0.        x3=0

 

Subtracting equation 2 from equation 1

 

-x2=0.         x2=0

 

So, x1= 1

 

So, solution is  

 

(1 0 0)