The given system of equations, in augmented matrix form can be written as follows

Now carry out Row operations R₂= R₂-R₁ and R₃=R₃-3R₁

.

Next R₃= R₃+4R₂ will yield , which is now in Reduced Row Echelon Form. From R₃ we have z= -1

From R₂ we have y+3z=-5, giving us y=-2

From R₁ we have x+y-z=0, giving us x= 1

Hence Solution is (x,y,z)= (1,-2,-1)