Question
\( -4 x+3 y=2 \) \( 3 x-9 y=3 \) Is \( (4,1) \) a solution of the system? Choose 1 answer: (A) Yes (B) No
Ask by Mills Whittaker. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\((4, 1)\) is not a solution to the system.
**Answer:**
**(B) No**
Solution
To determine if \((4, 1)\) is a solution to the given system of equations:
\[
\begin{cases}
-4x + 3y = 2 \\
3x - 9y = 3
\end{cases}
\]
**Step 1: Substitute \(x = 4\) and \(y = 1\) into the first equation.**
\[
-4(4) + 3(1) = -16 + 3 = -13 \neq 2
\]
The first equation does **not** hold true for \((4, 1)\).
**Step 2: Substitute \(x = 4\) and \(y = 1\) into the second equation.**
\[
3(4) - 9(1) = 12 - 9 = 3 = 3
\]
The second equation **does** hold true for \((4, 1)\).
**Conclusion:**
For \((4, 1)\) to be a solution to the system, it must satisfy **both** equations. Since it only satisfies the second equation and not the first, \((4, 1)\) is **not** a solution to the system.
**Answer:**
**(B) No**
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Simplify this solution Beyond the Answer
To check if \( (4,1) \) is a solution of the system, we substitute \( x = 4 \) and \( y = 1 \) into both equations. For the first equation: \( -4(4) + 3(1) = -16 + 3 = -13 \), which does not equal 2. For the second equation: \( 3(4) - 9(1) = 12 - 9 = 3 \), which equals 3. Since it does not satisfy the first equation, \( (4,1) \) is not a solution. The answer is: (B) No
