Chapter 11.1, Problem 46AYU

To determine

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

Answer to Problem 46AYU

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,

$\left(2x-3y-z\right)+\left(-x+2y+z\right)=0+5$

$2x-3y-z-x+2y+z=5$

$x-y=5$

Adding second and third equation we get,

$\left(-x+2y+z\right)+\left(3x-4y-z\right)=5+1$

$-x+2y+z+3x-4y-z=6$

$2x-2y=6$

$x-y=3$

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

This is not possible.

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