Chapter 11: Q. 49 (page 714)

solve each system of equations. If the system has no solution, say that it is inconsistent.
$2 x - 2 y + 3 z = 6 4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1$

Short Answer

Expert verified

The system is inconcsistent

Step by step solution

Given information

We are given a system of equation

$2 x - 2 y + 3 z = 6 (1) 4 x - 3 y + 2 z = 0 (2) - 2 x + 3 y - 7 z = 1 (3)$

Add equation 2 and 3

We get, $4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1 2 x - 5 z = 1$

Hence $2 x - 5 z = 1$

Multiply equation 1 by 3 and equation 3 by 2The add both the equation

We get,

$3 (2 x - 2 y + 3 z = 6) 6 x - 6 y + 9 z = 18 (4) 2 (- 2 x + 3 y - 7 z = 1) - 4 x + 6 y - 7 z = 2 (5)$

And on adding both the equations we get

$6 x - 6 y + 9 z = 18 - 4 x + 6 y - 14 z = 2 2 x - 5 z = 20$

Hence $2 x - 5 z = 20$

But in previous stem we got $2 x - 5 z = 1$

Hence the system is inconsistent

Conclusion

The 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.
$2 x - 2 y + 3 z = 6 4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1$

Short Answer

Step by step solution

Given information

Add equation 2 and 3

Multiply equation 1 by 3 and equation 3 by 2The add both the equation

Conclusion

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solve each system of equations. If the system has no solution, say that it is inconsistent.2x-2y+3z=64x-3y+2z=0-2x+3y-7z=1

Short Answer

Step by step solution

Given information

Add equation 2 and 3

Multiply equation 1 by 3 and equation 3 by 2The add both the equation

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

solve each system of equations. If the system has no solution, say that it is inconsistent.
$2 x - 2 y + 3 z = 6 4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1$