Answer:
All are correct.
Step-by-step explanation:
Let x be the number of movies and y be the number of newly released video games.
Larry has a gift card worth 400 for a local entertainment store Movies cost $20 each and newly released video games cost $50 each.
[tex]20x+50y\leq 400[/tex]
Larry must purchase at least nine items.
[tex]x+y\geq 9[/tex]
Check both inequalities of all given ordered pairs.
For (5,6),
[tex]20(5)+50(6)\leq 400\Rightarrow 400\leq 400[/tex]
[tex]5+6\geq 9\Rightarrow 16\geq 9[/tex]
Point (5,6) satisfy both inequalities.
For (10,4),
[tex]20(10)+50(4)\leq 400\Rightarrow 400\leq 400[/tex]
[tex]10+4\geq 9\Rightarrow 14\geq 9[/tex]
Point (10,4) satisfy both inequalities.
For (20,0),
[tex]20(20)+50(0)\leq 400\Rightarrow 400\leq 400[/tex]
[tex]20+0\geq 9\Rightarrow 20\geq 9[/tex]
Point (20,0) satisfy both inequalities.
For (15,2),
[tex]20(15)+50(2)\leq 400\Rightarrow 400\leq 400[/tex]
[tex]15+2\geq 9\Rightarrow 17\geq 9[/tex]
Point (15,2) satisfy both inequalities.
Therefore, all combination of movies and newly released video games Larry could purchase using his gift card.
