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Chapter 11: Q. 43 (page 714)

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

x-2y+3z=72x+y+z=4-3x+2y-2z=-10

Short Answer

Expert verified

The solution of the system of equation isx=2,y=-1,z=1

Step by step solution

01

Given information

We are given a system of equation

x-2y+3z=72x+y+z=4-3x+2y-2z=-10

02

Multiply equation 2 by 2

We get,

4x+2y+2z=8 (4)

Now add this to equation 2

We get,

x-2y+3z=7+4x+2y+2z=85x+5z=15

Hence

5x+5z=15x+z=3 (5)

Now subtract equation (4) from equation 3

-3x+2y-2z=-10-4x-2y-2z=-8-7x-4z=-18

-7x-4z=-18 (6)

03

Find the value of x

Multiply equation 5 by 4 And add it to equation 6

We get,

4x+4z=12

Now we add this to equation 6

We get,

4x+4z=12-7x-4z=-18-3x=-6

hencex=2

04

Find the value of y and z

We get,

x+z=32+z=3z=1

And

x-2y+3z=72-2y+3=7-2y=2y=-1

05

Conclusion

The solution of the system of equation isx=2,y=-1,z=1

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Most popular questions from this chapter

Verify that the values of the variables listed are solutions of the system of equations.

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