Write the solution of the linear system corresponding to the reduced augmented matrix. \[ \left[\begin{array}{rrr|r} 1 & 0 & -3 & 5 \\ 0 & 1 & 9 & -8 \end{array}\right] \] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The unique solution is \( x_{1}=\square, x_{2}=\square \), and \( x_{3}=\square \). \( \square \) \( \square \) \( \square \) (Simplify your answers.) B. The system has infinitely many solutions. The solution is \( x_{1}=\square, x_{2}=\square \), and \( x_{3}=t \). \( \square \) \( \square \) (Simplify your answers. Type expressions using \( t \) as the variable.) C. There is no solution.

From the given reduced augmented matrix, we can extract the equations representing the system. The first row gives us \( x_1 - 3x_3 = 5 \), and the second row gives us \( x_2 + 9x_3 = -8 \). By solving these equations, we find: 1. From the first equation, we can express \( x_1 \) as \( x_1 = 5 + 3x_3 \). 2. From the second equation, we express \( x_2 \) as \( x_2 = -8 - 9x_3 \). Thus, the solution can be expressed in terms of \( x_3 \): - \( x_1 = 5 + 3t \) - \( x_2 = -8 - 9t \) - \( x_3 = t \) This means the system has infinitely many solutions, where \( t \) is a free variable. The correct choice is B. The solution is \( x_{1}=5 + 3t, x_{2}=-8 - 9t \), and \( x_{3}=t \).