Solve this system using Gaussian Elimination with back-substitution.

x=

y=

z=

Write the augmented matrix for the system.

Switch E_{1}withE_{3}

Switch E_{2 }with E_{3}

E_{2}=E_{2}-2E_{1}

E_{3}=E_{3}-3E_{1}

E_{1}=E_{1}/2

E_{2}=E_{2}/4

E_{3}=E_{3}/10

The matrix is now in row-echelon form, and the corresponding system is

Using back substitution (z=0), we can determine that

y+z=1 , y=1-z

y=1-0=1

Using back substitution again (z=0 and y=1), we can determine that

x-1/2y-3/2z=3/2

x=3/2+1/2y+3/2z

x=3/2+1/2(1)+3/2(0)=3/2+1/2=2