Question

I have very bad luck doing these mainly because the steps are confusing. I really need some help with this one, otherwise I'm going to be up all night. PLEASE AND THANK YOU.

Solve this system of equations.

x+y+4z = 35

-5x+2y+z = -14

-7x+4y-3z = -48

Answer 1

First write augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	1	1	4	35
2	-5	2	1	-14
3	-7	4	-3	-48

Find the pivot in the 1st column in the 1st row

	X1	X2	X3	b
1	1	1	4	35
2	-5	2	1	-14
3	-7	4	-3	-48

Eliminate the 1st column

	X1	X2	X3	b
1	1	1	4	35
2	0	7	21	161
3	0	11	25	197

Make the pivot in the 2nd column by dividing the 2nd row by 7

	X1	X2	X3	b
1	1	1	4	35
2	0	1	3	23
3	0	11	25	197

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	1	12
2	0	1	3	23
3	0	0	-8	-56

Make the pivot in the 3rd column by dividing the 3rd row by -8

	X1	X2	X3	b
1	1	0	1	12
2	0	1	3	23
3	0	0	1	7

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	5
2	0	1	0	2
3	0	0	1	7

Solution set:

x = 5

y = 2

z = 7

(answer)