If `x - 4y = 1 and y = x//2 + 1`, then what is the value of x?

Options

A. `-5`
B. `-2`
C. `2`
D. `5`

Answer

To solve the equations \( x - 4y = 1 \) and \( y = \frac{x}{2} + 1 \), we will follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \( x - 4y = 1 \) (Equation 1)
2. \( y = \frac{x}{2} + 1 \) (Equation 2)

### Step 2: Substitute Equation 2 into Equation 1
We will substitute the expression for \( y \) from Equation 2 into Equation 1.

Substituting \( y \) in Equation 1:
\[ x - 4\left(\frac{x}{2} + 1\right) = 1 \]

### Step 3: Simplify the equation
Now, we will simplify the left side:
\[ x - 4\left(\frac{x}{2}\right) - 4(1) = 1 \]
This simplifies to:
\[ x - 2x - 4 = 1 \]

### Step 4: Combine like terms
Now, combine the terms involving \( x \):
\[ -x - 4 = 1 \]

### Step 5: Isolate \( x \)
Next, we will isolate \( x \) by adding 4 to both sides:
\[ -x = 1 + 4 \]
\[ -x = 5 \]

### Step 6: Solve for \( x \)
Now, multiply both sides by -1 to solve for \( x \):
\[ x = -5 \]

### Conclusion
Thus, the value of \( x \) is \( -5 \).

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