Check whether x=2 & y =-2 is a solution of 2x-y=6

Answer

To check whether \( x = 2 \) and \( y = -2 \) is a solution of the equation \( 2x - y = 6 \), we will follow these steps:

### Step 1: Write down the equation
The given equation is:
\[ 2x - y = 6 \]

### Step 2: Substitute the values of \( x \) and \( y \)
We need to substitute \( x = 2 \) and \( y = -2 \) into the equation. So we replace \( x \) with 2 and \( y \) with -2:
\[ 2(2) - (-2) = 6 \]

### Step 3: Simplify the left-hand side (LHS)
Now, we calculate the left-hand side:
\[ 2(2) = 4 \]
\[ -(-2) = +2 \]
Thus, the left-hand side becomes:
\[ 4 + 2 = 6 \]

### Step 4: Compare LHS and right-hand side (RHS)
Now we compare the left-hand side with the right-hand side:
\[ LHS = 6 \quad \text{and} \quad RHS = 6 \]

### Step 5: Conclusion
Since the left-hand side is equal to the right-hand side, we conclude that:
\[ 2x - y = 6 \quad \text{is satisfied by} \quad (x, y) = (2, -2) \]
Thus, \( x = 2 \) and \( y = -2 \) is indeed a solution of the equation.

---