Chapter 11: Q. 50 (page 714)

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

Short Answer

Expert verified

The system of equation is inconsistent

Step by step solution

Given information

We are given a system of equation

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

Add equation 1 and 2

We get,

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

We get, $- 4 x + y = 7 (4)$

Now multiply equation 2 by 2 and subtract from equation 3

We get,

$2 (7 x - 3 y + 2 z = - 1) 14 x - 6 y + 4 z = - 2$

Now we subtract

$14 x - 6 y + 4 z = - 2 + - 2 x + 3 y - 4 z = 0 12 x - 3 = - 2$

We get,

$12 x - 3 y = - 2 - 4 x + y = \frac{2}{3}$

But from previous step we have $- 4 x + y = 7$

As both equations cannot have different values The system of equation 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.
$3 x - 2 y + 2 z = 6 7 x - 3 y + 2 z = - 1 2 x - 3 y + 4 z = 0$

Short Answer

Step by step solution

Given information

Add equation 1 and 2

Now multiply equation 2 by 2 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.3x-2y+2z=67x-3y+2z=-12x-3y+4z=0

Short Answer

Step by step solution

Given information

Add equation 1 and 2

Now multiply equation 2 by 2 and subtract from equation 3

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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