5 votes 5 votes How many integer solutions are there to the system of inequalities$$x_{1}+x_{2}+x_{3}+x_{4} \leq 15, \quad x_{1}, \ldots, x_{4} \geq 0 ?$$ Combinatory goclasses_wq13 numerical-answers goclasses combinatory counting 1-mark + – GO Classes asked Jun 14, 2022 recategorized Jun 19, 2022 by Lakshman Bhaiya GO Classes 495 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
5 votes 5 votes We add one extra variable to turn the inequality to an equality: $$ x_{1}+x_{2}+x_{3}+x_{4}+s=15, \quad s, x_{i} \geq 0 . $$ This gives $\left(\begin{array}{c}15+5-1 \\ 5-1\end{array}\right)$ integer solutions. GO Classes answered Jun 14, 2022 GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.