Question

The number of solutions of equation $4x+9y=119$ is (x, y $\in$ non-negative integers)

• A. 4
• B. 6
• C. 2
• D. 3

Answer 1

The correct option is D 3

Consider: $4x+9y=119$
At $x=0;4\left(0\right)+9y=119$
$\Rightarrow y=\frac{119}{9}$
Thus, y $\notin$ non-negative integer.
At x = 1; 4(1) + 9y = 119
$\Rightarrow 9y=119-4$
$\Rightarrow y=\frac{115}{9}$
Thus, y $\notin$ non-negative integer.
At x = 2; 4(2) + 9y = 119
$\Rightarrow 9y=119-8$
$\Rightarrow y=\frac{111}{9}$
Thus, y $\notin$ non-negative integer.
At x = 5; 4(5) + 9y = 119
$\Rightarrow 9y=119-20$
$\Rightarrow y=\frac{99}{9}=11$
Thus, y $\in$ non-negative integer.
Similarly, for x = 14 and x = 30, y $\in$ non-negative integer. Thus, there are three solutions for which x and y are non-negative integers.
Hence, the correct answer is option (d).