Find the solution set of each linear system Identify inconsi

Find the solution set of each linear system. Identify inconsistent systems and dependent equations.

x+2y-z=3

x+3y+z-7

x-5y+3z=-7

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The system is consistent and the solution set is StartSet left parenthesis nothing comma nothing comma nothing right parenthesis EndSet , , . (Simplify your answers. Use integers or fractions for any numbers in the expression.) B. The system is consistent and dependent. The solution set is the set of all ordered triples StartSet left parenthesis nothing comma nothing comma z right parenthesis EndSet , ,z, where z is any real number. (Type an expression using z as the variable.) C. The system is inconsistent

Solution

Your matrix

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

Eliminate the 1st column

Find the pivot in the 2nd column in the 2nd row

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 18

Eliminate the 3rd column

solution

x = 0

y = 2

z = 1

unique solution