Question

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination.If the system has an infinite number of solutions, express x, y, and z in terms of the parameter t.)

3x + 3y + 9z = 6

x + y + 3z = 2

2x + 5y + 15z = 10

-x + 2y + 6z = 4

(x, y, z) = ?

Answer 1

Augmented matrix for given system of equations

Your matrix

	X1	X2	X3	b
1	3	3	9	6
2	1	1	3	2
3	2	5	15	10
4	-1	2	6	4

Find the pivot in the 1st column and swap the 2nd and the 1st rows

	X1	X2	X3	b
1	1	1	3	2
2	3	3	9	6
3	2	5	15	10
4	-1	2	6	4

Eliminate the 1st column

	X1	X2	X3	b
1	1	1	3	2
2	0	0	0	0
3	0	3	9	6
4	0	3	9	6

Make the pivot in the 2nd column by dividing the 3rd row by 3 and swap the 3rd and the 2nd rows

	X1	X2	X3	b
1	1	1	3	2
2	0	1	3	2
3	0	0	0	0
4	0	3	9	6

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	0	0
2	0	1	3	2
3	0	0	0	0
4	0	0	0	0

Solution set:

x = 0

y = 2 - 3t

z = t, t = free parameter

(x,y,z) = (0, 2 - 3t, t) (answer)