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. $$ \begin{array}{l} \left\{\begin{array}{l} -8 x+4 y=24 \ -7 x+7 y=28 \end{array}\right. \ x=\square \end{array} $$

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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 **$$-2$$**.
$$ x = -2 $$

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