B) Check whether \( (6,9) \) is a solution of the systems of linear equations. \begin{tabular}{ll} 5) \( s+7 t=69 \) & 6) \( \begin{array}{l}-2 p+5 q=34 \\ -7 q=-61-8 p \\ 6 t+4 s=73\end{array} \) \\ \hline\end{tabular}

To check whether \( (6,9) \) is a solution for the equations, we need to substitute \( s = 6 \) and \( t = 9 \) into the first equation and \( p \) and \( q \) into the second system. 1. For the first equation \( s + 7t = 69 \): \[ 6 + 7(9) = 6 + 63 = 69 \] This is true! 2. For the second system of equations, we need to find \( p \) and \( q \) such that \( (p, q) \) satisfies: - \( -2p + 5q = 34 \) - \( -7q = -61 - 8p \) - \( 6t + 4s = 73 \) Substituting \( s = 6 \) and \( t = 9 \) into the third equation: \[ 6(9) + 4(6) = 54 + 24 = 78 \] Since \( 78 \neq 73 \), \( (6, 9) \) is not a solution to the system of equations. Thus, the answer is confirmed: \( (6, 9) \) is a solution for the first equation, but not for the second system.