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Chapter 11: Q. 48 (page 714)

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

2x-3y-z=03x+2y+2z=2x+5y+3z=2

Short Answer

Expert verified

The solution set for the given system is{(x,y,z)=(6-4z13,4-7z13,z)/z鈭�R}

Step by step solution

01

Given information

We are given an equation

2x-3y-z=0(1)3x+2y+2z=2(2)x+5y+3z=2(3)

02

Multiply equation 1 by 2 and equation 2 by 3And then add both the equation

We get,

2(2x-3y-z=0)4x-6y-2z=0(4)3(3x+2y+2z=2)9x+6y+6z=5(5)

Now we add both the equation

4x-6y-2z=0+9x+6y+6z=413x+4z=4

Hence we have

13x+4z=4x=4-4z13

03

Multiply equation 1 by 3 and then add it to equation 3

We get,

3(2x-3y-z=0)6x-9y-3z=0

And now we add,

3x+2y+2z=2-3x-15y-9z=-6-13y-7z=-4

Hence we get,-13y-7z=-4y=-7z+413

04

Conclusion

The solution set for the given equation is

{(x,y,z)=(6-4z13,4-7z13,z)/z鈭�R}

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