Solution of the equation 3x-y=3 is

Options

A. (0,-3)
B. (2,3)
C. (3,6)
D. All of these

Answer

To determine the solutions of the equation \(3x - y = 3\), we will check each of the given points to see if they satisfy the equation.

### Step-by-Step Solution:

1. **Identify the equation**: We have the equation \(3x - y = 3\).

2. **Check the first point**: Let's check the point \((0, -3)\).
- Substitute \(x = 0\) and \(y = -3\) into the equation:
\[ 3(0) - (-3) = 3 \]
- Simplifying this gives:
\[ 0 + 3 = 3 \]
- Since \(3 = 3\), the point \((0, -3)\) is a solution.

3. **Check the second point**: Now, check the point \((2, 3)\).
- Substitute \(x = 2\) and \(y = 3\) into the equation:
\[ 3(2) - 3 = 3 \]
- Simplifying this gives:
\[ 6 - 3 = 3 \]
- Since \(3 = 3\), the point \((2, 3)\) is also a solution.

4. **Check the third point**: Finally, check the point \((3, 6)\).
- Substitute \(x = 3\) and \(y = 6\) into the equation:
\[ 3(3) - 6 = 3 \]
- Simplifying this gives:
\[ 9 - 6 = 3 \]
- Since \(3 = 3\), the point \((3, 6)\) is also a solution.

5. **Conclusion**: All the points \((0, -3)\), \((2, 3)\), and \((3, 6)\) satisfy the equation \(3x - y = 3\). Therefore, they are all solutions to the equation.