Chapter 11: Q. 52 (page 714)

Solve each system of equations. If the system has no solution, say that it is inconsistent
x - y + z = -4
2x - 3y + 4z = -15
5x + y - 2z = 12

Short Answer

Expert verified

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

Step by step solution

Given information

We are given a system of equation

x - y + z = -4 (1)

2x - 3y + 4z = -15 (2)

5x + y - 2z = 12 (3)

Add equation 1 and 3

We get,

$x - y + z = - 4 + 5 x + y - 2 z = 12 6 x - z = 8$

We get $6 x - z = 8 (4)$

Now multiply equation 3 by 3 and add it to equation 2

We get,

$3 (5 x + y - 2 z = 12) 15 x + 3 y - 6 z = 36$

Now we add the equations

$2 x - 3 y + 4 x = - 15 + 15 x + 3 y - 6 z = 36 17 x - 2 z = 21$

We get, $17 x - 2 z = 21$ (5)

Multiply equation 4 by 2 and subtract equation 5 from it

We get,

$2 (6 x - z = 8) 12 x - 2 z = 16$

Now we subtract from equation 5 from it

$12 x - 2 z = 16 - 17 x + 2 z = - 21 - 5 x = - 5$

Hence $x = 1$

Find the values of y and z

We get,

$6 x - z = 8 6 - z = 8 z = - 2$

Similarly

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

Hence the solution set of system is ${(x, y, z) = (1, 3, - 2)}$

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Solve each system of equations. If the system has no solution, say that it is inconsistent
x - y + z = -4
2x - 3y + 4z = -15
5x + y - 2z = 12

Short Answer

Step by step solution

Given information

Add equation 1 and 3

Multiply equation 4 by 2 and subtract equation 5 from it

Find the values of y and z

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Solve each system of equations. If the system has no solution, say that it is inconsistentx - y + z = -42x - 3y + 4z = -155x + y - 2z = 12

Short Answer

Step by step solution

Given information

Add equation 1 and 3

Multiply equation 4 by 2 and subtract equation 5 from it

Find the values of y and z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Discrete Mathematics

Probability and Statistics

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each system of equations. If the system has no solution, say that it is inconsistent
x - y + z = -4
2x - 3y + 4z = -15
5x + y - 2z = 12