Khan Academy Donate streak, so let's start a new one today. week Level 4 (i) Find the solution to the system of equations. You can use the interactive graph below to find the solution. \[ \begin{array}{l} \left\{\begin{array}{l} -8 x+4 y=24 \\ -7 x+7 y=28 \end{array}\right. \\ x=\square \end{array} \]

Sure, let's solve the system of equations step by step to find the value of \( x \). **Given System:** \[ \begin{cases} -8x + 4y = 24 \quad \text{(Equation 1)} \\ -7x + 7y = 28 \quad \text{(Equation 2)} \end{cases} \] **Step 1: Simplify Both Equations** - **Simplify Equation 1:** Divide every term by 4 to make the coefficients smaller. \[ \frac{-8x}{4} + \frac{4y}{4} = \frac{24}{4} \\ -2x + y = 6 \quad \text{(Simplified Equation 1)} \] - **Simplify Equation 2:** Divide every term by 7. \[ \frac{-7x}{7} + \frac{7y}{7} = \frac{28}{7} \\ -x + y = 4 \quad \text{(Simplified Equation 2)} \] **Step 2: Solve for One Variable** Let's solve for \( y \) in both equations: - **From Simplified Equation 1:** \[ -2x + y = 6 \\ y = 2x + 6 \quad \text{(Expression A)} \] - **From Simplified Equation 2:** \[ -x + y = 4 \\ y = x + 4 \quad \text{(Expression B)} \] **Step 3: Set the Two Expressions for \( y \) Equal to Each Other** \[ 2x + 6 = x + 4 \] **Step 4: Solve for \( x \)** \[ 2x + 6 = x + 4 \\ 2x - x = 4 - 6 \\ x = -2 \] **Step 5: Find \( y \) Using the Value of \( x \)** Plug \( x = -2 \) into **Expression B**: \[ y = (-2) + 4 \\ y = 2 \] **Solution:** \[ x = -2 \quad \text{and} \quad y = 2 \] So, the value to fill in the blank for \( x \) is **\(-2\)**.