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The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x\leq y$ is  __________

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 $: 13$

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