Final answer:
To solve the system using row reduction on a calculator, represent the system as an augmented matrix and perform row reduction operations. The solution is (-4, -4, 3)
Step-by-step explanation:
To solve the system using row reduction on a calculator, we need to represent the given system of equations as an augmented matrix. The augmented matrix for the system is:
[[2, 3, 6, -2], [1, -2, 4, 16], [3, -5, 0, 8]]
Next, we need to perform row reduction operations on the matrix to obtain its row echelon form or reduced row echelon form. After performing the row reduction operations, we get:
[[1, 0, 2, -4], [0, 1, -2, 4], [0, 0, 0, 0]]
The row echelon form of the augmented matrix corresponds to the system of equations:
x + 2z = -4
y - 2z = 4
0 = 0
From the last row, we can see that there is a free variable, z. We can express the solutions in terms of z as follows:
x = -4 - 2z
y = 4 + 2z
So, the solution to the system is given by (-4 - 2z, 4 + 2z, z), where z can take any value. Therefore, the correct answer is option B. (-4, -4, 3).