Chapter 11: Q. 53 (page 714)

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

Short Answer

Expert verified

The solution set of given system is ${(x, y, z) = (- 3, \frac{1}{2}, 1)}$

Step by step solution

Given information

We are given a system of equation

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

Add equation 2 and 3

We get,

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

Hence we get $- 2 y - 2 x = 3 (4)$

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

We get,

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

Also

$2 x + 4 y - 2 z = - 6 + - 2 x + 2 y - 3 z = 4 6 y - 5 z = - 2$

Hence $6 y - 5 z = - 2 (5)$

Multiply equation 4 by 3 and add it to equation 5

We get,

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

Also

$6 y - 5 z = - 2 + - 6 y - 6 z = - 9 - 11 z = - 11$

Hence $z = 1$

Find the values of x and y

We get,

$2 y + 2 z = 3 2 y + 2 = 3 2 y = 1 y = \frac{1}{2}$

Also

$x + 2 y - z = - 3 x + 1 - 1 = - 3 x = - 3$

The solution set is ${(x, y, z) = (- 3, \frac{1}{2}, 1)}$

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

Short Answer

Step by step solution

Given information

Add equation 2 and 3

Multiply equation 4 by 3 and add it to equation 5

Find the values of x and y

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Solve each system of equations. If the system has no solution, say that it is inconsistent x + 2y - z = -32x - 4y + z = -7-2x + 2y - 3z = 4

Short Answer

Step by step solution

Given information

Add equation 2 and 3

Multiply equation 4 by 3 and add it to equation 5

Find the values of x and y

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Decision Maths

Statistics

Logic and Functions

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 + 2y - z = -3
2x - 4y + z = -7
-2x + 2y - 3z = 4