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Chapter 11: Q. 44 (page 714)

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

2x+y-3z=0-2x+2y+z=-73x-4y-3z=7

Short Answer

Expert verified

The solution of the system of equation isx=5613,y=-713,z=3513

Step by step solution

01

Given information

We are given a system of equations

2x+y-3z=0-2x+2y+z=-73x-4y-3z=7

02

Multiply equation 2 by 3 

We get,

-6x+6y+3z=-21 (4)

Now add equation 1 and 4

We get,

2x+y-3z=0-6x+6y+3z=-21-4x+7y=-21

Hence-4x+7y=-21

Now we add equation 4 and 3

We get,

3x-4y-3z=7-6x+6y+3z=-21-3x+2y=-14

We get,-3x+2y=-14

03

Now we solve equation 4 and 5

We get,

-12x+21y=-63+12x-8y=5613y=-7

Hence we get y=-713

04

Find the value x and z

We get,

3x=2y+143x=2(-713)+143x=-1413+143x=16813x=5613

Similarly

2x+y-3z=03z=2x+y3z=2(5613)-7133z=10513z=3513

05

Conclusion

The solution of the equation arex=5613,y=-713,z=3513

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