Chapter 11.1, Problem 45AYU

To determine

To find: The solution of the given system of equations.

Answer to Problem 45AYU

Solution:

No solution exists; Inconsistent.

Explanation of Solution

Given:

  $x-y-z=1$

  $2x+3y+z=2$

  $3x+2y=0$

Calculation:

The system of equations is:

  $x-y-z=1$

  $2x+3y+z=2$

  $3x+2y=0$

Adding first and second equation we get,

  $(x-y-z)+(2x+3y+z)=1+2$

  $x-y-z+2x+3y+z=3$

  $3x+2y=3$

The third equation is $3x+2y=0$ .

In both the above equations LHS is same as $3x+2y$ , but RHS have different values ( 3 and 0 ).

This is not possible.

Therefore the solution to this system of equations does not exist, inconsistent system.