If `x-9=2y and x+3=5y`, what is the value of x?

Options

A. `-2`
B. `4`
C. `11`
D. `17`

Answer

To solve the equations \( x - 9 = 2y \) and \( x + 3 = 5y \) to find the value of \( x \), we can follow these steps:

### Step 1: Rearrange the second equation to express \( y \) in terms of \( x \).
From the equation \( x + 3 = 5y \), we can isolate \( y \):
\[ y = \frac{x + 3}{5} \]

### Step 2: Substitute the expression for \( y \) into the first equation.
Now we substitute \( y \) from Step 1 into the first equation \( x - 9 = 2y \):
\[ x - 9 = 2\left(\frac{x + 3}{5}\right) \]

### Step 3: Simplify the equation.
Multiply both sides by 5 to eliminate the fraction:
\[ 5(x - 9) = 2(x + 3) \]
Expanding both sides gives:
\[ 5x - 45 = 2x + 6 \]

### Step 4: Rearrange the equation to isolate \( x \).
Subtract \( 2x \) from both sides:
\[ 5x - 2x - 45 = 6 \]
This simplifies to:
\[ 3x - 45 = 6 \]

### Step 5: Solve for \( x \).
Add 45 to both sides:
\[ 3x = 6 + 45 \]
\[ 3x = 51 \]
Now, divide both sides by 3:
\[ x = \frac{51}{3} = 17 \]

### Final Answer:
The value of \( x \) is \( 17 \).

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