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 determine whether the point \( (6, 9) \) is a solution to the given systems of linear equations, we'll examine each system separately. --- ### **Problem 5** **Equation:** \[ s + 7t = 69 \] **Given Point:** \[ (t, s) = (6, 9) \] **Substitution:** \[ s + 7t = 9 + 7 \times 6 = 9 + 42 = 51 \] **Comparison:** \[ 51 \neq 69 \] **Conclusion:** The point \( (6, 9) \) **does not** satisfy equation 5. --- ### **Problem 6** **System of Equations:** \[ \begin{cases} -2p + 5q = 34 \\ -7q = -61 - 8p \\ 6t + 4s = 73 \\ \end{cases} \] **Given Point:** Assuming \( (p, q, t, s) = (6, 9, 6, 9) \) **Checking Each Equation:** 1. **First Equation:** \[ -2p + 5q = -2 \times 6 + 5 \times 9 = -12 + 45 = 33 \] \[ 33 \neq 34 \] 2. **Second Equation:** \[ -7q = -7 \times 9 = -63 \] \[ -61 - 8p = -61 - 8 \times 6 = -61 - 48 = -109 \] \[ -63 \neq -109 \] 3. **Third Equation:** \[ 6t + 4s = 6 \times 6 + 4 \times 9 = 36 + 36 = 72 \] \[ 72 \neq 73 \] **Conclusion:** The point \( (6, 9) \) **does not** satisfy any of the equations in system 6. --- ### **Final Verdict** The point \( (6, 9) \) is **not** a solution to either of the given systems of linear equations.