Given that, equation $2x+y = 40$
$\Rightarrow \boxed{y= 40-2x ; x \le y \longrightarrow (1)}$
Put the various values of $x$ in equation $(1),$ and get the number of solutions.
- $x=1 \Rightarrow y=38$
- $x=2 \Rightarrow y=36$
- $x=3 \Rightarrow y=34$
- $x=4 \Rightarrow y=32$
- $x=5 \Rightarrow y=30$
- $x=6 \Rightarrow y=28$
- $x=7 \Rightarrow y=26$
- $x=8 \Rightarrow y=24$
- $x=9 \Rightarrow y=22$
- $x=10 \Rightarrow y=20$
- $x=11 \Rightarrow y=18$
- $x=12 \Rightarrow y=16$
- $x=13 \Rightarrow y=14$
- $x=14 \Rightarrow y=12$ $(x \le y)$ Conditions Violated
$\therefore$ The number of solutions of the equation $2x+y=40$ is $13.$
Correct Answer $: 13$