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}

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UpStudy AI · Accepted Answer

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.
The point $$ (6, 9) $$ is **not** a solution to either system of equations. **System 5:** - Substituting $$ t = 6 $$ and $$ s = 9 $$ into $$ s + 7t = 69 $$ gives $$ 9 + 42 = 51 $$, which does not equal 69. **System 6:** - Substituting $$ p = 6 $$, $$ q = 9 $$, $$ t = 6 $$, and $$ s = 9 $$ into each equation: - First equation: $$ -2(6) + 5(9) = -12 + 45 = 33 \neq 34 $$ - Second equation: $$ -7(9) = -63 $$ and $$ -61 - 8(6) = -109 $$, so $$ -63 \neq -109 $$ - Third equation: $$ 6(6) + 4(9) = 36 + 36 = 72 \neq 73 $$ Therefore, $$ (6, 9) $$ does not satisfy any of the equations in either system.

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}

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