To solve the system of equations given:
- \( 3x + 3y = 15 \)
- \( 8x + 5y = 46 \)
We can simplify the first equation:
- \( 3x + 3y = 15 \) can be simplified by dividing everything by 3:
\[ x + y = 5 \quad (1) \]
Now we have a simpler equation (1) and the second equation remains the same (2):
- \( 8x + 5y = 46 \)
Now we can express \( y \) from equation (1):
\[ y = 5 - x \quad (3) \]
Next, we substitute equation (3) into equation (2):
\[ 8x + 5(5 - x) = 46 \]
Expanding:
\[ 8x + 25 - 5x = 46 \]
Now, combine like terms:
\[ 3x + 25 = 46 \]
Next, subtract 25 from both sides:
\[ 3x = 21 \]
Now, divide by 3:
\[ x = 7 \]
Now that we have \( x \), we can find \( y \) using equation (3):
\[ y = 5 - x = 5 - 7 = -2 \]
Thus, the solution to the system of equations is \( x = 7 \) and \( y = -2 \).
Looking at the options provided, the correct answer is:
B \( x = 7, y = -2 \)