Chapter 11.1, Problem 16AYU

$\{\begin{array}{l}4x-\text{ 5}z=\text{ 6}\\ \text{5}y-z=-17\\ -x-\text{ 6}y+\text{ 5}z=24\end{array}$

$x=\text{ 4},y=-3;z=\text{ 2};\left(4,-3,2\right)$

To determine

The solution of the given system of equations.

Answer to Problem 16AYU

$\left(x,y\right)=\left(4,-3,2\right)$ is the solution.

Explanation of Solution

Given:

$4x-5z=6$

$5y-z=-17$

$-x-6y+5z=24$

$x=4,y=-3,z=2$

Calculation:

The system of equations is,

$4x-5z=6$

$5y-z=-17$

$-x-6y+5z=24$

For $x=4,y=-3,z=2$ we have,

First equation: $4\left(4\right)-5\left(2\right)=16-10=6$

Second equation: $5\left(-3\right)-2=-15-2=-17$

Third equation: $-4-6\left(-3\right)+5\left(2\right)=-4+18+10=24$

Therefore the values $x=4,y=-3,z=2$ satisfy all these three given equations and hence is the solution of the given system of equations.