Put the below system of linear equations into triangular for

Put the below system of linear equations into triangular form and solve the system if possible. Classify the system as consistent independent, consistent dependent, or inconsistent.

x + y + z = 3

2x y + z = 0

4x + 4y + 6z = 4

Solution

x + y + z = 3

2x y + z = 0

4x + 4y + 6z = 4

Adding first and third equations we get

x+y+z+2x-y+z=3

3x +2z=3

Multiply first by -4 and add it to third equation we get

-4x-4y-4z-4x+4y+6z=-12+4

-8x+2z=-8

-4x +z=-4

Now we have two equations

3x + 2z=3

-4x+z=-4

Multiply second by -2 and add it to first we get

3x+8x=3+8

11x=11

x=1

-4x+z=-4

-4+z=-4

z=0

x+y+z=3

1+y+0=3

y=2

So the solution is (1,2,0)

And since we are getting a single solution hence it is consistent and independent system