Questions: The matrix below is the final matrix form for a system of two linear equations in the variables (x1) and (x2). Write the solution of the system. [ left[beginarrayrrr 1 0 -9 0 1 6 endarrayright] ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The unique solution to the system is (x1=) and (x2=) B. There are infinitely many solutions. The solution is (x1=) and (x2=t) for any real number (t). (Type an expression using (t) as the variable.) C. There is no solution.

Solution Steps

To solve the system of equations represented by the given matrix, we need to interpret the matrix in terms of the variables \(x_1\) and \(x_2\). The matrix is in reduced row-echelon form, which directly gives the values of the variables. The first row indicates that \(x_1 = -9\) and the second row indicates that \(x_2 = 6\). Therefore, the system has a unique solution.

The given matrix is in reduced row-echelon form, which represents the system of equations: \[ \begin{align*}

1. & \quad x_1 = -9 \\
2. & \quad x_2 = 6 \end{align*} \]

From the matrix, we can directly read the values of the variables:

• The first equation gives us \(x_1 = -9\).
• The second equation gives us \(x_2 = 6\).

Final Answer