Question

If x and y are whole numbers and 2x + y = 5, then the total number of possible solutions of this equation is

• A. 0
• B. 2
• C. 1
• D. 3

Answer 1

The correct option is D 3

Given: $2x+y=5$
At $x=0;2\left(0\right)+y=5$
$\Rightarrow y=5$ (Whole number)
At $x=1;2\left(1\right)+y=5$
$\Rightarrow y=5–2=3$ (Whole number)
At $x=2;2\left(2\right)+y=5$
$\Rightarrow y=5–4=1$ (Whole number)
At $x=3;2\left(3\right)+y=5$
$\Rightarrow y=5–6=–1$ (Not a whole number)
The given equation is a linear equation, therefore, for values of x greater than or equal to 3, the values of y will be negative, i.e., not a whole number.
Thus, only possible solutions of $2x+y=5$, where x and y are whole numbers are $(0,5),(1,3)$ and $(2,1)$.
Hence, the correct answer is option (d).