Check whether (1,-2) is solution of 2x-y =6

Answer

To check whether the point (1, -2) is a solution of the equation \(2x - y = 6\), we will substitute the values of \(x\) and \(y\) from the point into the equation and see if both sides are equal.

### Step-by-step Solution:

1. **Identify the equation and the point**:
- The equation is \(2x - y = 6\).
- The point is \((1, -2)\), where \(x = 1\) and \(y = -2\).

2. **Substitute the values of \(x\) and \(y\) into the equation**:
- Replace \(x\) with \(1\) and \(y\) with \(-2\) in the equation:
\[ 2(1) - (-2) = 6 \]

3. **Simplify the left-hand side (LHS)**:
- Calculate \(2(1)\):
\[ 2(1) = 2 \]
- Now, calculate \(-(-2)\):
\[ -(-2) = 2 \]
- Therefore, the left-hand side becomes:
\[ 2 + 2 = 4 \]

4. **Compare LHS with the right-hand side (RHS)**:
- The right-hand side (RHS) of the equation is \(6\).
- Now, we compare:
\[ LHS = 4 \quad \text{and} \quad RHS = 6 \]

5. **Conclusion**:
- Since \(LHS \neq RHS\) (4 is not equal to 6), the point \((1, -2)\) does not satisfy the equation \(2x - y = 6\).
- Therefore, \((1, -2)\) is not a solution of the equation.

### Final Answer:
The point \((1, -2)\) is not a solution of the equation \(2x - y = 6\).