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Chapter 11: Q. 14 (page 713)

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

4x-z=78x+5y-z=0-x-y+5z=6x=2,y=-3,z=1;2,-3,1

Short Answer

Expert verified

The given values are the solutions because all equations are true for the given values.

Step by step solution

01

Step 1. Given information.

The given equations are:

4x-z=78x+5y-z=0-x-y+5z=6

The given solution is x=2,y=-3,z=1or 2,-3,1.

02

Step 2. Check the solution.

If all equations are true for the given values, then the values represent the solution.

Substitute x=2,y=-3,z=1in the first equation.

4(2)-(1)=8-1=7

So, the first equation is true.

Substitute x=2,y=-3,z=1in the second equation.

8(2)+5(-3)-(1)=16-15-1=0

So, the second equation is true.

Substitute x=2,y=-3,z=1in the third equation.

-(2)-(-3)+5(1)=-2+3+5=6

So, the third equation is true.

03

Step 3. Conclusion.

The given values are the solutions because all equations are true for the given values.

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