Question
Find the solution to the system of equations given below. \( x=-4 \) \( -5 x-4 y=16 \) (A) \( (-4,1) \) (B) \( (4,1) \) (C) \( (-4,-1) \) (D) \( (4,-1) \)
Ask by Rose Hamilton. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( (-4, 1) \), choice A.
Solution
To solve the system of equations:
1. **Given Equations:**
\[
\begin{cases}
x = -4 \\
-5x - 4y = 16
\end{cases}
\]
2. **Substitute \( x = -4 \) into the second equation:**
\[
-5(-4) - 4y = 16
\]
\[
20 - 4y = 16
\]
3. **Solve for \( y \):**
\[
-4y = 16 - 20
\]
\[
-4y = -4
\]
\[
y = 1
\]
4. **Solution:**
\[
(x, y) = (-4, 1)
\]
**Answer:** (A) \( (-4,1) \)
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Simplify this solution Extra Insights
To solve this system of equations, we can substitute \( x = -4 \) into the second equation. Starting with the equation: \[ -5(-4) - 4y = 16 \] This simplifies to: \[ 20 - 4y = 16 \] Now, subtract 20 from both sides: \[ -4y = 16 - 20 \] \[ -4y = -4 \] Next, divide both sides by -4: \[ y = 1 \] So, the solution to the system of equations is \( (-4, 1) \). The correct answer is (A) \( (-4, 1) \).
