Question

Write the solution of the equation \( 3x + y = 11 \) in natural numbers.

Hint:

Natural Number Solutions: Solve for integer values that satisfy the equation.

Answer 1

We need integer solutions where \( x, y \) are natural numbers.
Rearrange:
\[ y = 11 - 3x \] For natural \( y \), \( 11 - 3x>0 \Rightarrow x<\frac{11}{3} \approx 3.67 \).
Possible integer values:
\[ x = 1, y = 8 \quad (1,8) \] \[ x = 2, y = 5 \quad (2,5) \] \[ x = 3, y = 2 \quad (3,2) \] Thus, the natural number solutions are \( \mathbf{(1,8), (2,5), (3,2)} \).
Correct Answer: \( (1, 8), (2, 5), (3, 2) \)