Final answer:
To find the value of y in the solution to the system of equations represented by the given matrix, use matrix operations and row operations to solve the augmented matrix.
Step-by-step explanation:
To find the value of y in the solution to the system of equations represented by the given matrix, we can use matrix operations.
We can represent the system of equations as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
In this case, A = [[1, 0, 0, y],[1, -2, -1, 0],[8, 4, 6, 1]], X = [[x],[y],[z],[1]], and B = [[1],[0],[0]].
To find the value of y, we need to solve the augmented matrix [A|B] using row operations.
After performing row operations to put the augmented matrix in reduced row-echelon form, we find that the value of y is 2.