x=5 and y=2 is a solution of the linear equation

Options

A. `x+2y=7`
B. `5x+2y=7`
C. `x+y=7`
D. `5x+y=7`

Explanation

To determine which linear equation has the solution \( x = 5 \) and \( y = 2 \), we can substitute these values into the given options and check which one holds true.

### Step-by-Step Solution:

1. **Identify the given values**: We have \( x = 5 \) and \( y = 2 \).

2. **Check the first equation**: Let's assume the first equation is \( x + y = 7 \).
- Substitute \( x \) and \( y \) into the equation:
\[ 5 + 2 = 7 \]
- Calculate the left side:
\[ 7 = 7 \]
- This equation is true, so \( x + y = 7 \) is a valid equation.

3. **Check the second equation**: Let's assume the second equation is \( x + y = 9 \).
- Substitute \( x \) and \( y \) into the equation:
\[ 5 + 2 = 9 \]
- Calculate the left side:
\[ 7 \neq 9 \]
- This equation is false, so \( x + y = 9 \) is not a valid equation.

4. **Check the third equation**: Let's assume the third equation is \( x + y = 29 \).
- Substitute \( x \) and \( y \) into the equation:
\[ 5 + 2 = 29 \]
- Calculate the left side:
\[ 7 \neq 29 \]
- This equation is false, so \( x + y = 29 \) is not a valid equation.

5. **Check the fourth equation**: Let's assume the fourth equation is \( x + y = 7 \) (which we already checked).
- We have already determined that this equation holds true.

### Conclusion:
The linear equation that has the solution \( x = 5 \) and \( y = 2 \) is:
\[ x + y = 7 \]