Chapter 11.1, Problem 46AYU

To determine

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

Answer to Problem 46AYU

Solution:

No solution exists; Inconsistent.

Explanation of Solution

Given:

  $2x-3y-z=0$

  $-x+2y+z=5$

  $3x-4y-z=1$

Calculation:

The system of equations is:

  $2x-3y-z=0$

  $-x+2y+z=5$

  $3x-4y-z=1$

Adding first and second equation we get,

  $(2x-3y-z)+(-x+2y+z)=0+5$

  $2x-3y-z-x+2y+z=5$

  $x-y=5$

Adding second and third equation we get,

  $(-x+2y+z)+(3x-4y-z)=5+1$$-x+2y+z+3x-4y-z=6$

  $2x-2y=6$

  $x-y=3$

Thus the equations $x-y=5$ and $x-y=3$ both have LHS as same as $x-y$ , but RHS have different values ( 5 and 3 ).

This is not possible.

Therefore the solution to this system of equations does not

exist, inconsistent system.