Determine whether $$ (5,-2) $$ is a solution of $$ 6 q-7 p=48 $$. Unless stated otherwise, to determine whether an ordered pair is a solution of an equation, use the first number in the ordered pair to replace the variable that occurs first alphabetically. Use the second number in the ordered pair to replace the other variable. The variable $$ p $$ occurs first alphabetically amongst the variables in the given equation. So substitute $$ \square $$ for $$ p $$ and $$ \square $$ for $$ q $$ in the equation $$ 6 q-7 p=48 $$.

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To determine whether the ordered pair $$ (5, -2) $$ is a solution of the equation $$ 6q - 7p = 48 $$, we will follow these steps:

1. Identify the variables in the equation: $$ p $$ and $$ q $$.
2. Substitute the values from the ordered pair into the equation, where $$ p = 5 $$ and $$ q = -2 $$.

Now, we will substitute $$ p $$ and $$ q $$ into the equation:

$$
6q - 7p = 48
$$

Substituting $$ p = 5 $$ and $$ q = -2 $$:

$$
6(-2) - 7(5) = 48
$$

Now, we will perform the calculations step by step:

1. Calculate $$ 6(-2) $$:
   $$
   6(-2) = -12
   $$

2. Calculate $$ -7(5) $$:
   $$
   -7(5) = -35
   $$

3. Combine the results:
   $$
   -12 - 35 = -47
   $$

Now we compare the result with 48:

$$
-47 \neq 48
$$

Since the left side does not equal the right side, the ordered pair $$ (5, -2) $$ is **not** a solution of the equation $$ 6q - 7p = 48 $$.
$$ (5, -2) $$ is not a solution of the equation $$ 6q - 7p = 48 $$.

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