Question

Use? Cramer's rule to solve the system of equations. If

D equals=?0, use another method to determine the solution set

5x+5y-15z=9

5x+y-z=7

-x-y+3z=4

Answer 1

Determinant of the main matrix is zero. This means that the system of linear equations is either inconsistent or has infinitely many solutions. Gauss-Jordan elimination method will help get the complete answer.

D= 0

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	5	5	-15	9
2	5	1	-1	7
3	-1	-1	3	4

Find the pivot in the 1st column (inversing the sign in the whole row) and swap the 3rd and the 1st rows

	X1	X2	X3	b
1	1	1	-3	-4
2	5	1	-1	7
3	5	5	-15	9

Eliminate the 1st column

	X1	X2	X3	b
1	1	1	-3	-4
2	0	-4	14	27
3	0	0	0	29

Make the pivot in the 2nd column by dividing the 2nd row by -4

	X1	X2	X3	b
1	1	1	-3	-4
2	0	1	-7/2	-27/4
3	0	0	0	29

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	1/2	11/4
2	0	1	-7/2	-27/4
3	0	0	0	29

Solution set:

The system is inconsistent