The value of x and y from the equation `3x-y=3 and 9x-3y=9` are

Options

A. One solution
B. No solution
C. Infinite solution
D. Noen of these.

Answer

To solve the system of equations given by:

1. \( 3x - y = 3 \) (Equation 1)
2. \( 9x - 3y = 9 \) (Equation 2)

we can follow these steps:

### Step 1: Simplify the second equation
Notice that the second equation can be simplified. We can divide the entire equation by 3:

\[ 9x - 3y = 9 \implies 3x - y = 3 \]

This means that Equation 2 is actually the same as Equation 1.

### Step 2: Identify the type of solution
Since both equations are identical (i.e., \( 3x - y = 3 \)), this indicates that there are infinitely many solutions. The two equations represent the same line in the coordinate plane.

### Step 3: Express one variable in terms of the other
We can express \( y \) in terms of \( x \) using Equation 1:

\[ 3x - y = 3 \implies y = 3x - 3 \]

### Step 4: General solution
The general solution can be expressed as:

\[ (x, y) = (x, 3x - 3) \quad \text{for any real number } x \]

### Conclusion
Thus, the solution set is infinite, and for any value of \( x \), we can find a corresponding value of \( y \).