studentkakraaLv1

25 Aug 2022

First photo is the main question, the example is shown in the other photo.

Solve the system of equations.

 

 

Select the correct choice below and fill in any answer boxes within your choice.

A. The one solution is x = ____, y = ____, and z = ____. (Simplify your answers.)

B. There are infinitely many solutions. If z is allowed to be any real number, then x= ____ and y = ___ (Type expressions using z as the variable.)

C. There is no solution.

 

Solve the system of equations.

 

 

 

To eliminate the x-item from the second equation. Multiply both sides of the first equation by - 1 and add the result to the second equation.

 

     

Now use the sarse method so eirrinale the x-term in the third equation

Multiply both sides of the first equation by -1 and add the result in the third equation.

 

 

 

The equivalent system with the new second and third equations is shown below. The next step is to eliminate the y-term from the third equation.

 

     

 

To eliminate the y-item from the third equation. Multiply both sides of the second equation by 11 and add the result to the third equation.

 

 

 

Finally, to obtain an x-coefficient of 1 in the this equation multiply both sides of the third equation by  

 

 

The system is now in echelon form. Solve by back-substitute.

 

 

 

The third equation gives the value of a

Back-substitute 2 tor z in the second equation and solve for y: