$$ -4 x+3 y=2 $$ $$ 3 x-9 y=3 $$ Is $$ (4,1) $$ a solution of the system? Choose 1 answer: (A) Yes (B) No

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UpStudy AI · Accepted Answer

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**
$$(4, 1)$$ is not a solution to the system. **Answer:** **(B) No**

Is a solution of the system?
Choose 1 answer:
(A) Yes
(B) No

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Is a solution of the system? Choose 1 answer: (A) Yes (B) No