x=2 ,y=3 is a solution of the linear equation

Options

A. 2x+y=8
B. x+2y=8
C. x+y=8
D. `-x+y=8`

Answer

To determine if the pair \( (x, y) = (2, 3) \) is a solution to the given linear equations, we will substitute \( x = 2 \) and \( y = 3 \) into each equation and check if both sides are equal.

### Step-by-Step Solution:

1. **Equation 1: \( 2x + y = 8 \)**
- Substitute \( x = 2 \) and \( y = 3 \):
\[ 2(2) + 3 = 4 + 3 = 7 \]
- Compare with the right-hand side:
\[ 7 \neq 8 \]
- Conclusion: \( (2, 3) \) is **not** a solution for this equation.

2. **Equation 2: \( x + 2y = 8 \)**
- Substitute \( x = 2 \) and \( y = 3 \):
\[ 2 + 2(3) = 2 + 6 = 8 \]
- Compare with the right-hand side:
\[ 8 = 8 \]
- Conclusion: \( (2, 3) \) **is** a solution for this equation.

3. **Equation 3: \( x + y = 8 \)**
- Substitute \( x = 2 \) and \( y = 3 \):
\[ 2 + 3 = 5 \]
- Compare with the right-hand side:
\[ 5 \neq 8 \]
- Conclusion: \( (2, 3) \) is **not** a solution for this equation.

4. **Equation 4: \( -2x + y = 1 \)**
- Substitute \( x = 2 \) and \( y = 3 \):
\[ -2(2) + 3 = -4 + 3 = -1 \]
- Compare with the right-hand side:
\[ -1 \neq 1 \]
- Conclusion: \( (2, 3) \) is **not** a solution for this equation.

### Final Conclusion:
The pair \( (x, y) = (2, 3) \) is a solution for the equation \( x + 2y = 8 \).

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