Chapter 11: Q. 46 (page 714)

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$2 x - 3 y - z = 0 - x + 2 y + z = 5 3 x - 4 y - z = 1$

Short Answer

Expert verified

The given system of equation is inconsistent

Step by step solution

Given information

We are given a system of equation

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

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

We get,

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

Also

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

We get $y + z = 10 (4)$

Multiply equation 2 by 3 and subtract from equation 3

We get,

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

Also

$- 3 x + 6 y + 3 z = 15 + 3 x - 4 y - z = 1 2 y + 2 z = 16$

We get

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

But from 4 we have $y + z = 10$

Same equations cannot have different values

Hence the system is inconsistent

Conclusion

The given system of equation is inconsistent

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Solve each system of equations. If the system has no solution, say that it is inconsistent.
$2 x - 3 y - z = 0 - x + 2 y + z = 5 3 x - 4 y - z = 1$

Short Answer

Step by step solution

Given information

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

Multiply equation 2 by 3 and subtract from equation 3

Conclusion

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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

Step by step solution

Given information

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

Multiply equation 2 by 3 and subtract from equation 3

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Applied Mathematics

Statistics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$2 x - 3 y - z = 0 - x + 2 y + z = 5 3 x - 4 y - z = 1$