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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

01

Given information

We are given a system of equation

x - y + z = -4 (1)

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

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

02

Add equation 1 and 3

We get,

x-y+z=-4+5x+y-2z=126x-z=8

We get 6x-z=8(4)

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

We get,

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

Now we add the equations

2x-3y+4x=-15+15x+3y-6z=3617x-2z=21

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

03

Multiply equation 4 by 2 and subtract equation 5 from it

We get,

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

Now we subtract from equation 5 from it

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

Hencex=1

04

Find the values of y and z

We get,

6x-z=86-z=8z=-2

Similarly

x-y+z=-41-y-2=-4y=3

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

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Most popular questions from this chapter

The ratio of a to b is 4:3. The sum of a and b is 14. What is the ratio of a-b to a+b?

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