Question
Solve the system of equations using the elimination method and enter the value of \( y \). \[ \begin{array}{c}4 x-5 y=-9 \\ -4 x+y=-7\end{array} \]
Ask by Hardy Jimenez. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( y = 4 \)
Solution
To solve the system of equations using the elimination method, follow these steps:
Given:
\[
\begin{cases}
4x - 5y = -9 \quad \text{(Equation 1)} \\
-4x + y = -7 \quad \text{(Equation 2)}
\end{cases}
\]
**Step 1:** Add Equation 1 and Equation 2 to eliminate \( x \).
\[
4x - 5y + (-4x + y) = -9 + (-7)
\]
Simplify:
\[
0x - 4y = -16
\]
\[
-4y = -16
\]
**Step 2:** Solve for \( y \).
\[
y = \frac{-16}{-4} = 4
\]
**Answer:** \( y = 4 \)
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Simplify this solution The Deep Dive
To solve the system of equations using the elimination method, we can start by adding both equations together to eliminate \( x \). 1. The original equations are: \[ 4x - 5y = -9 \quad \text{(1)} \] \[ -4x + y = -7 \quad \text{(2)} \] 2. Let's add equations (1) and (2): \[ (4x - 5y) + (-4x + y) = -9 - 7 \] This simplifies to: \[ -4y = -16 \] 3. Now, divide both sides by -4: \[ y = 4 \] Thus, the value of \( y \) is \( 4 \).
