Question

Ð. Solve the following system of linear equations by Gaussian elimination:

4x + 4y + 4z = 8

2x + y + z = 3

2x - 2y + 6z = 16

Show all your work and explain every step of the process.

Answer 1

4x+4y+4z=8
2x+y+z=3
2x-2y+6z=16

Step 1 - Divide the 1st equation by 4 and 3rd equation by 2. The resulting equations are:

x+y+z=2
2x+y+z=3
x-y+3z=8

Step 2 - Multiply 1st equation with -1 and add with 2nd equation. The resulting 2nd equation is:
x+y+z=2
x=1
x-y+3z=8

Step 3 - Substituting the x value i.e 1 to the 1st and 3rd equation and the resultng equations are :

y+z=1

x=1
-y+3z=7

Step 4 - Adding 1st equation with 3rd equation and the resulting equations are:

y+z=1

x=1
z=2

Step 5 - Substituting z value i.e 2 in 1st equation results in

y=-1

x=1

z=2

Hence, values are (x,y,z) = (1,-1,2)