Q. 81 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 75– 82, algebraically solve each system of equations using any method you wish.

$\left\{\begin{array}{l}2x-3y+z=4\\ -3x+2y-z=17\\ -5y+z=6\end{array}\right.$

Step-by-Step Solution

Answer

The given equations $\left\{\begin{array}{l}2x-3y+z=4\\ -3x+2y-z=17\\ -5y+z=6\end{array}\right.$ has no solution.Hence the system is inconsistent

Step 1. Given information

The given equations $\left\{\begin{array}{l}2x-3y+z=4\\ -3x+2y-z=17\\ -5y+z=6\end{array}\right.$

Step 2. Finding the values of x , y   a n d   z

Consider the equations $2x-3y+z=4,-3x+2y-z=17$ and$-5y+z=6$ .To solve these equations,it seems easiest to eliminate the variable z first.So,we add the first two equations 

$2x-3y+z=4+-3x+2y-z=17-x-y=21$

$-x-y=21 \cdots \cdots \cdots \cdots \left(1\right)$

Again we add the last two equations

$-3x+2y-z=17+-5y+z=6-3x-3y=23$

$-3x-3y=23 \cdots \cdots \left(2\right)$

Now we multiplay equation (1) by 3 and then substract equation (2) from it

$-3x-3y=63-3x-3y=230x+0y=46$

$0x+0y=46 \cdots \cdots \cdots \left(3\right)$

Equation (3) has no solution.Hence the system is inconsistent