Q. 79 - Precalculus Enhanced with Graphing Utilities

Question

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

$\left\{\begin{array}{l}5x-y+4z=2\\ -x+5y-4z=3\\ 7x+13y-4z=17\end{array}\right.$

Step-by-Step Solution

Answer

The given equation $\left\{\begin{array}{l}5x-y+4z=2\\ -x+5y-4z=3\\ 7x+13y-4z=17\end{array}\right.$ has no solution.Hence the system is incosistent

Step 1. Given inforrmation

The given equations $\left\{\begin{array}{l}5x-y+4z=2\\ -x+5y-4z=3\\ 7x+13y-4z=17\end{array}\right.$

Step 2. Finding the values of x,y and z

Consider the equations $5x-y+4z=2,-x+5y-4z=3$and $7x+13y-4z=17$.To solve these equations,it seems easiest to eliminate the variable first.So,we add the first two equations

$5x-y+4z=2+-x+5y-4z=34x+4y+0z=5$     

$4x+4y+0z=5 \dots \dots \left(1\right)$

Now,we substract the last equation from the second equation

$--x+5y-4z=37x+13y-4z=17-8x-8y+0z=-14$

$-8x-8y+0z=-14 \cdots \cdots \left(2\right)$

We multiplay equation (1) by 2 and equation (2)

$8x+8z=10-8x-8y=140x+0y=-4$

$0x+0y=-4 \cdots \cdots \left(3\right)$

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