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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,-83,19)}

Step by step solution

01

Given information

We are given a system of equations

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

02

Add equation 1 and 2

We get,

x+4y-3z=-8+3x-y+3z=124x+3y=4

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

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

We get,

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

Also

2x+8x-6z=-16+x+y+6z=13x+9y=-15

Hence we get

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

03

Subtract equation 4 and 5

We get,

4x+3y=4-x-3y=53x=9

hence x=3

04

Find the values of y and z

We get,

x+3y=-53+3y=-53y=-8y=-83

Now also we have

x+4y-3z=-8-3+4(-83)-3z=-8z=19

The solution set is{(x,y,z)=(-3,-83,19)}

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