Answer:
[tex]\left\{\begin{array}{l}x\ge 0\\ \\y\ge 0\\ \\2x+y\le 15\end{array}\right.[/tex]
Step-by-step explanation:
Let x be the number of lily bulbs and y be the number of tulip bulbs Kenji bought. Note that [tex]x\ge 0, \ y\ge 0.[/tex]
Lily bulbs cost $4 each, then x lily bulbs cost $4x.
Tulip bulbs cost $2 each, then y tulip bulbs cost $2y.
In total, x lily bulbs and y tulip bulbs cost [tex]\$(4x+2y).[/tex]
Kenji has at most $30 to spend on lily bulbs and tulip bulbs at his local flower store, so
[tex]4x+2y\le 30\\ \\2x+y\le 15[/tex]
So, you get the system of three inequalities:
[tex]\left\{\begin{array}{l}x\ge 0\\ \\y\ge 0\\ \\2x+y\le 15\end{array}\right.[/tex]
Attached diagram shows the solution set - triangle with verticis (0,0), (0,15) and (7.5,0). All points inside this triangle are the solutions (possible numbers of lily bulbs, x, and tulip bulbs, y).
