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Chapter 11: Q. 50 (page 714)

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

3x-2y+2z=67x-3y+2z=-12x-3y+4z=0

Short Answer

Expert verified

The system of equation is inconsistent

Step by step solution

01

Given information

We are given a system of equation

3x-2y+2z=6(1)7x-3y+2z=-1(2)2x-3y+4z=0(3)

02

Add equation 1 and 2

We get,

3x-2y+2z=6-7x+3y-2z=1-4x+y=7

We get,-4x+y=7(4)

03

Now multiply equation 2 by 2 and subtract from equation 3

We get,

2(7x-3y+2z=-1)14x-6y+4z=-2

Now we subtract

14x-6y+4z=-2+-2x+3y-4z=012x-3=-2

We get,

12x-3y=-2-4x+y=23

But from previous step we have -4x+y=7

As both equations cannot have different values The system of equation is inconsistent

04

Conclusion

The system of equation is inconsistent

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

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