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Chapter 11: Q. 42 (page 714)

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

2x+y=4-2y+4z=03x-2z=-11

Short Answer

Expert verified

The solution of the system of equation is

x=-3y=2z=1

Step by step solution

01

Given information

We are given a system of equation

2x+y=4-2y+4z=03x-2z=-11

02

multiply equation 1 by 2 and add it to the equation 2

We get,

4x+2y=-8

And now

4x+2y=-8+-2y+4z=04x+4z=-8

03

Now we Multiply equation 3 by 2 and add it the new equation

We get,

4x+4z=-8+6x-4z=-2210x=-30

And hence role="math" localid="1646827256666" x=-3

04

Substitute the value of x to find the value of y,z

We get,

2x+y=-42(-3)+y=-4-6+y=-4y=2

Similarly

3x-2z=-113(-3)-2z=-11-9-2z=-11-2z=-2z=1

05

Conclusion

The solution of the system of equation isx=-3,y=2,z=1

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