Question

Cody has $7. He wants to

buy at least 4 snacks. Hot
dogs (x) are $2 each.
Peanuts (y) are $1 each.
Which ordered pair is a
solution?
x + y 24
2x + y s7
1,1 or 1,3

Answer 1

Answer: (1,3)

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Step-by-step explanation:

Note that the two shaded regions overlap to form the darker shaded region. The point (1,1) is only in the green region, but not in the blue region. It needs to be in both regions for it to be a solution to the system. In contrast, the point (1,3) is on the boundary of the blue region and in the green region as well. It's a solution point because of this.

Points on the boundary are included because of the "or equal to" as part of the inequality sign. Hence the solid boundary lines rather than dashed boundary lines.

The solution (1,3) means that x = 1 and y = 3 pair up together. It says that Cody can buy x = 1 hotdog and y = 3 packs of peanuts so that he has at least 4 snacks, and he stays within the $7 budget.

Going back to (x,y) = (1,1) for a moment, this isn't a solution because x+y = 1+1 = 2 is not 4 or larger. In other words, he only buys 2 snacks here instead of 4 or more.