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Chapter 11: Q. 46 (page 714)

Solve each system of equations. If the system has no solution, say that it is inconsistent.

2x-3y-z=0-x+2y+z=53x-4y-z=1

Short Answer

Expert verified

The given system of equation is inconsistent

Step by step solution

01

Given information

We are given a system of equation

2x-3y-z=0(1)-x+2y+z=5(2)3x-4y-z=1(3)

02

Multiply equation 2 by 2 and subtract from equation 1 we get,

We get,

2(-x+2y+z=5)-2x+4y+2z=10

Also

-2x+4y+2z=10+2x-3y-z=0y+z=10

We gety+z=10(4)

03

Multiply equation 2 by 3 and subtract from equation 3

We get,

3(-x+2y+z=5)-3x+6y+3z=15

Also

-3x+6y+3z=15+3x-4y-z=12y+2z=16

We get

2y+2z=16y+z=8(5)

But from 4 we have y+z=10

Same equations cannot have different values

Hence the system is inconsistent

04

Conclusion

The given system of equation is inconsistent

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