Solve the system, if possible. x+y -z=-6 Select the correct choice below and, if

Question

Solve the system, if possible. x+y -z=-6 Select the correct choice below and, if necessary, fll in the answer box to complete your choice. OA The solutions(EAWD O B. There are infinitely many solutions. The solutions are ), where z is any real number. Type exact answers in simplified form.) Type exact answers in simplified form.) du O C. There is no solution odu Click to select and enter your answer(s). This course (MATOSSCO3 Algebraic Literacy Su18 (Carol Kramer) is based on Colorado Community Colleges Online: M Copyright 2018 Pearson Education 0 FS 2 4

Explanation / Answer

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

1

1

-1

-6

-1

0

1

1

0

1

3

4

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

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

Add -1 times the 2nd row to the 3rd row

Multiply the 3rd row by 1/3

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

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

Then the RREF of A is

1

0

0

2

0

1

0

-5

0

0

1

3

Now, since the row operations do not affect the solution to a linear system of equations, hence, the given linear system of equations is equivalent to /has the solution x = 2, y = -5 and z = 3. Option A is the correct answer. The solution is (x,y,z) = (2,-5,3).

1

1

-1

-6

-1

0

1

1

0

1

3

4

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