Question
\begin{tabular}{|l|l} Determine whether \( (9,-2) \) is a solution of \( 5 p-3 q=51 \). & \( \begin{array}{l}\text { Is }(9,-2) \text { is a solution of the equation } \\ 5 p-3 q=51 \text { ? } \\ \text { O Yes } \\ \text { O No }\end{array} \)\end{tabular}
Ask by Hodgson Santiago. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( (9, -2) \) is a solution of the equation \( 5p - 3q = 51 \).
Solution
\[
\text{Let } (p,q) = (9,-2).
\]
\[
\text{Substitute } p = 9 \text{ and } q = -2 \text{ into the equation } 5p - 3q = 51:
\]
\[
5(9) - 3(-2) = 45 + 6 = 51.
\]
\[
\text{Since } 51 = 51, \text{ the point } (9,-2) \text{ satisfies the equation.}
\]
\[
\boxed{\text{Yes}}
\]
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Simplify this solution Bonus Knowledge
To determine if the point \( (9,-2) \) is a solution to the equation \( 5p - 3q = 51 \), we simply substitute \( p = 9 \) and \( q = -2 \) into the equation: \[ 5(9) - 3(-2) = 45 + 6 = 51 \] Since both sides of the equation equal 51, this means \( (9, -2) \) is indeed a solution. So, the answer is: Yes!
