Question

Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), and z = t. If there is no solution, enter NO SOLUTION.) 2x + 3y − z = −1 x + 2y = 5 x + 3y + z = 12

Answer 1

inconsistent

Explanation:

The sum of the first and last equations is ...

(2x +3y -z) +(x +3y +z) = (-1) +(12)

3x +6y = 11

Three times the second equation is ...

3(x +2y) = 3(5)

3x +6y = 15

There are no values of x, y, or z that can make both of these equations true. They are inconsistent.