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Chapter 11: Q. 79 (page 757)

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

5x-y+4z=2-x+5y-4z=37x+13y-4z=17

Short Answer

Expert verified

The given equation5x-y+4z=2-x+5y-4z=37x+13y-4z=17 has no solution.Hence the system is incosistent

Step by step solution

01

Step 1. Given inforrmation

The given equations5x-y+4z=2-x+5y-4z=37x+13y-4z=17

02

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

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

localid="1647429180260" 5x-y+4z=2+-x+5y-4z=34x+4y+0z=5

4x+4y+0z=5鈥�鈥�(1)

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鈰�鈰�(2)

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

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

0x+0y=-4鈰�鈰�(3)

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

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