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

Question

Solve the system of equations. If the system has no solution, say that it is inconsistent. 5x - 2y z1 x 3y 2z-11 Select the correct choice below and fill in any answer boxes within your choice. O A. The solution of the system is xy and z B. There are infinitely many solutions. Using ordered triplets, the solution can be written as {xy,z)lx-yz any real number OC. There are infinitely many solutions. Using ordered triplets, the solution can be written as (xyz)lxy any real number, z any real number? O D. The system is inconsistent. (Simplify your answers.) (Simplify your answers. Type expressions using z as the variable as needed.) (Simplify your answer. Type an expression using y and z as the variables as needed.)

Explanation / Answer

The augmented matrix of the given system of linear equations is A (say) =

1

1

-1

5

5

-2

1

-1

1

3

-2

11

To solve the given system of linear equations, we will reduce A to its RREF as under:

Add -5 times the 1st row to the 2nd row

Add -1 times the 1st row to the 3rd row

Multiply the 2nd row by -1/7

Add -2 times the 2nd row to the 3rd row

Multiply the 3rd row by 7/5

Add 6/7 times the 3rd row to the 2nd row

Add 1 times the 3rd row to the 1st row

Add -1 times the 2nd row to the 1st row

Then the RREF of A is

1

0

0

1

0

1

0

2

0

0

1

-2

It implies that the given system of linear equations has a unique solution x = 1,y = 2 and z = -2.

Option A.

1

1

-1

5

5

-2

1

-1

1

3

-2

11

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