Solve the system of equations using the elimination method and enter the value of $$ y $$. $$ \begin{array}{c}4 x-5 y=-9 \ -4 x+y=-7\end{array} $$

Question

UpStudy AI · Accepted Answer

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:** $$ y = 4 $$
$$ y = 4 $$

Solve the system of equations using the elimination method and enter the value of \( y \). \[ \begin{array}{c}4 x-5 y=-9 \\ -4 x+y=-7\end{array} \]