Solve the following system of linear equations: 3x1+6x2+6x3 = -9 -2x1–3x2-3x3 = 3 if the system has infinitely many solutions, your answer may use expressions involving the parameters r, s, and t. o the system has at least one solution x1 = 0 x2 = 0 x3 = 0 o o

The system has infinite solutions and the set the solutions is  

Step-by-step explanation:

Consider the augmented matrix of the system: .

Now we will find the reduced echelon form of the matrix.

1. We subtract from row 2, 2/3 of row 1 and we obtain the matrix .

2.  We multiply the row 1 of the matrix that we obtained in the previous step by 1/3 and we obtain the matrix that is the reduced echelon form of the system matrix.

Now we use backward substitution for find the solution:

Observe that the matrix reduced echelon form of the system matrix has a free variable, then the system has infinite solutions.

1. , then

2. , replacing the value of x_2,

Then the set of solutions is

12r - 8 - 12

you have to combine like terms. below i have bolded the like terms:

12r - 8 - 12

together it combines to:

12r - 20

hope this !