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Chapter 11: Q. 51 (page 714)

solve each system of equations. If the system has no solution, say that it is inconsistent.

x + y - z = 6

3x - 2y + z = -5

x + 3y - 2z = 14

Short Answer

Expert verified

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

Step by step solution

01

Given information

We are given a system of equations

x + y - z = 6 (1)

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

x + 3y - 2z = 14 (3)

02

Subtract equation 1 and 3

We get,

x+y-z=6-x-3y+2z=-14-2y+z=-8

We get-2y+z=-8 (4)

03

Multiply equation 1 by 3 and then subtract from equation 2

We get,

3(x+y-z=6)3x+3y-3z=18(5)

Now subtract from equation (4)

3x+3y-3z=18-3x+2y-z=55y-4z=23

hence we get,5y-4z=23 (6)

04

Multiply equation 4 by 4 And add equation 6 

We get,

4(-2y+z=-8)-8y+4z=-32

Now we add equation 6 to it

-8y+4z=-32+5y-4z=23-3y=-9

hence y=3

05

Find the values of x and z

We have,

-2y+z=-8-2(3)+z=-8-6+z=-8z=-2

Now substitute the values of y and z in equation 1

x+y-z=6x+3-(-2)=6x+3+2=6x=1

hence solution of the system is (1,3,-2).

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