1. To start solving the system of equations below, which number would you multiply the equation \( -2 x-5 y=-1 \) by \( \left\{\begin{array}{c}-2 x-5 y=-1 \\ 8 x+4 y=16\end{array}\right. \) 2 4

To solve the system of equations using the **elimination method**, you typically aim to eliminate one of the variables by making their coefficients opposites. Let's analyze the given system: \[ \begin{cases} -2x - 5y = -1 \quad \text{(Equation 1)} \\ 8x + 4y = 16 \quad \text{(Equation 2)} \end{cases} \] **Step 1: Decide Which Variable to Eliminate** Let's choose to eliminate \( y \). - **Coefficient of \( y \) in Equation 1:** -5 - **Coefficient of \( y \) in Equation 2:** 4 To make these coefficients opposites, find the Least Common Multiple (LCM) of 5 and 4, which is 20. **Step 2: Determine the Multipliers** - Multiply **Equation 1** by **4** to get: \[ 4(-2x - 5y) = 4(-1) \implies -8x - 20y = -4 \] - Multiply **Equation 2** by **5** to get: \[ 5(8x + 4y) = 5(16) \implies 40x + 20y = 80 \] **Step 3: Add the Equations to Eliminate \( y \)** \[ (-8x - 20y) + (40x + 20y) = -4 + 80 \implies 32x = 76 \implies x = \frac{76}{32} = \frac{19}{8} \] **Conclusion:** To eliminate \( y \) initially, you should **multiply Equation 1 by 4**. **Answer:** 4