`3x-y/3=21`
`x=y+7`
Which ordered pair (x,y) satisfies the system of equations shown above?

Options

A. (0,-7)
B. (4,27)
C. (7,0)
D. (9,-16)

Answer

To solve the system of equations given by:

1. \( \frac{3x - y}{3} = 21 \)
2. \( x = y + 7 \)

we will follow these steps:

### Step 1: Simplify the first equation
Start with the first equation:

\[ \frac{3x - y}{3} = 21 \]

Multiply both sides by 3 to eliminate the fraction:

\[ 3x - y = 63 \]

### Step 2: Rewrite the second equation
The second equation is already in a simple form:

\[ x = y + 7 \]

We can also rewrite it as:

\[ x - y = 7 \]

### Step 3: Set up the system of equations
Now we have the following two equations:

1. \( 3x - y = 63 \) (Equation 1)
2. \( x - y = 7 \) (Equation 2)

### Step 4: Use elimination method
We will eliminate \( y \) by subtracting Equation 2 from Equation 1.

Subtract Equation 2 from Equation 1:

\[ (3x - y) - (x - y) = 63 - 7 \]

This simplifies to:

\[ 3x - y - x + y = 63 - 7 \]

### Step 5: Simplify the equation
Now combine like terms:

\[ 2x = 56 \]

### Step 6: Solve for \( x \)
Divide both sides by 2:

\[ x = 28 \]

### Step 7: Substitute \( x \) back into the second equation
Now substitute \( x = 28 \) into the second equation \( x = y + 7 \):

\[ 28 = y + 7 \]

### Step 8: Solve for \( y \)
Subtract 7 from both sides:

\[ y = 28 - 7 = 21 \]

### Step 9: Write the ordered pair
Thus, the ordered pair \( (x, y) \) that satisfies both equations is:

\[ (x, y) = (28, 21) \]

### Final Answer
The ordered pair that satisfies the system of equations is \( (28, 21) \).

---