Chapter 11: Q. 48 (page 714)

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

Short Answer

Expert verified

The solution set for the given system is ${(x, y, z) = (\frac{6 - 4 z}{13}, \frac{4 - 7 z}{13}, z) / z \in R}$

Step by step solution

Given information

We are given an equation

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

Multiply equation 1 by 2 and equation 2 by 3And then add both the equation

We get,

$2 (2 x - 3 y - z = 0) 4 x - 6 y - 2 z = 0 (4) 3 (3 x + 2 y + 2 z = 2) 9 x + 6 y + 6 z = 5 (5)$

Now we add both the equation

$4 x - 6 y - 2 z = 0 + 9 x + 6 y + 6 z = 4 13 x + 4 z = 4$

Hence we have

$13 x + 4 z = 4 x = \frac{4 - 4 z}{13}$

Multiply equation 1 by 3 and then add it to equation 3

We get,

$3 (2 x - 3 y - z = 0) 6 x - 9 y - 3 z = 0$

And now we add,

$3 x + 2 y + 2 z = 2 - 3 x - 15 y - 9 z = - 6 - 13 y - 7 z = - 4$

Hence we get, $- 13 y - 7 z = - 4 y = \frac{- 7 z + 4}{13}$

Conclusion

The solution set for the given equation is

${(x, y, z) = (\frac{6 - 4 z}{13}, \frac{4 - 7 z}{13}, z) / z \in R}$

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

Short Answer

Step by step solution

Given information

Multiply equation 1 by 2 and equation 2 by 3And then add both the equation

Multiply equation 1 by 3 and then add it to equation 3

Conclusion

One App. One Place for Learning.

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Solve each system of equations. If the system has no solution, say that it is inconsistent.2x-3y-z=03x+2y+2z=2x+5y+3z=2

Short Answer

Step by step solution

Given information

Multiply equation 1 by 2 and equation 2 by 3And then add both the equation

Multiply equation 1 by 3 and then add it to equation 3

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Calculus

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

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