Chapter 11: Q. 54 (page 714)

solve each system of equations. If the system has no solution, say that it is inconsistent
x + 4y - 3z = -8
3x - y + 3z = 12
x + y + 6z = 1

Short Answer

Expert verified

The solution of the system can be given as ${(x, y, z) = (- 3, - \frac{8}{3}, \frac{1}{9})}$

Step by step solution

Given information

We are given a system of equations

$x + 4 y - 3 z = - 8 (1) 3 x - y + 3 z = 12 (2) x + y + 6 z = 1 (3)$

Add equation 1 and 2

We get,

$x + 4 y - 3 z = - 8 + 3 x - y + 3 z = 12 4 x + 3 y = 4$

Hence we get, $4 x + 3 y = 4$ (4)

Now Multiply equation 1 by 2 and add it to equation 3

We get,

$2 (x + 4 y - 3 z = - 8) 2 x + 8 y - 6 z = - 16$

Also

$2 x + 8 x - 6 z = - 16 + x + y + 6 z = 1 3 x + 9 y = - 15$

Hence we get

$3 x + 9 y = - 15 x + 3 y = - 5 (5)$

Subtract equation 4 and 5

We get,

$4 x + 3 y = 4 - x - 3 y = 5 3 x = 9$

hence x=3

Find the values of y and z

We get,

$x + 3 y = - 5 3 + 3 y = - 5 3 y = - 8 y = - \frac{8}{3}$

Now also we have

$x + 4 y - 3 z = - 8 - 3 + 4 (- \frac{8}{3}) - 3 z = - 8 z = \frac{1}{9}$

The solution set is ${(x, y, z) = (- 3, - \frac{8}{3}, \frac{1}{9})}$

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solve each system of equations. If the system has no solution, say that it is inconsistent
x + 4y - 3z = -8
3x - y + 3z = 12
x + y + 6z = 1

Short Answer

Step by step solution

Given information

Add equation 1 and 2

Subtract equation 4 and 5

Find the values of y and z

One App. One Place for Learning.

Most popular questions from this chapter

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solve each system of equations. If the system has no solution, say that it is inconsistentx + 4y - 3z = -83x - y + 3z = 12x + y + 6z = 1

Short Answer

Step by step solution

Given information

Add equation 1 and 2

Subtract equation 4 and 5

Find the values of y and z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

solve each system of equations. If the system has no solution, say that it is inconsistent
x + 4y - 3z = -8
3x - y + 3z = 12
x + y + 6z = 1