Answer:
The system of equations can be expressed like
[tex]\left\{\begin{matrix}h+d=120\\ 3h-d=0\end{matrix}\right.[/tex]
Step-by-step explanation:
System of Two Linear Equations
It refers to situations where conditions are given in the form
[tex]\left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.[/tex]
Where x and y are the unknown variables and a,b,c,d,e,f are known constants
The problem describes a situation where one event space imposes two restrictions on a dog-themed party. The first one is there can only be 120 dogs and humans combined. Being h the number of humans, and d the number of dogs, then
[tex]h+d=120[/tex]
The other condition is there must be 1 human to every 3 dogs, we can model it by
[tex]d=3h[/tex]
Rearranging:
[tex]3h-d=0[/tex]
The system of equations can be expressed like
[tex]\left\{\begin{matrix}h+d=120\\ 3h-d=0\end{matrix}\right.[/tex]
Note: The solution of the system is h=30 humans and d=90 dogs
