Question

Can someone please help? It's the last one i'm stuck on

How do you solve the following equation by Gaussian Elimination, then indicate if the system is inconsistent or has an infinite number of solution?
x + y + x = 0
x + y = 3
y + z = 1

Answer 1

Given, x+x+y=0 or 2x+y=0 or 2x=-y
hence, x=-y/2
In the second equation, by substitution, we get, -y/2+y=3
Or, (-y+2y)/2=3
Or, y=6
hence, x=-6/2=-3
Also given that y+z=1
Or, 6+z=1
Hence, z=1-6=-5
Therefore, y=6, z=-5, x=-3