Question

Sheena and her friend want to form a team to play recreational soccer. They want a combination of males and females for the soccer team. They want to have no more than seven players on your team.

Part A: write a inequality to represent the situation
Part B: graph the inequality and shade the area where the possible solutions would lie.
Part C: what is the difference between the ordered pairs that fall on the line and the ones that fall in the unshaded area?

Answer 1

`x+y<7`

Explanation:

In this problem,
`x` will represent males, and
`y` will represent females.

So, the problem states that they don't want more than seven players, gender is not actually restricted here, just the total number per team. This means that the sum of both genders has to be less than 7. Then, the expression would be:

`x+y<7`

This expression expresses perfectly the relation asked by the problem. In words, it says that males plus women are less than 7.

If we graph this inequality, would be like the image attached.

As you can see in the graph, there's a important difference between a ordered pair that fall on the line, and other pair under the line. Basically, all ordered pairs that falls on the line, it means that they aren't solution for the inequality. Those pair that falls inside the shaded zone, those are solutions of the inequality, that's the difference.

Therefore, all solution are those ordered pairs that fall in the shaded zone.

Answer 2

Answer: The answer of all parts are mentioned below.

Explanation:

Let x represents the number of males and y represents the number of of males in a team.

Then According to the question, They want to have no more than seven players on your team.

Therefore, x + y < 7,

Which the required inequality to represents the given situation.

Since, For making the shaded region, we must take x≥0 and y≥0

( because number of males and females can not be negative)

Thus, the system of equation which describes the given condition is,

x + y < 7, x≥0 and y≥0

Since, if a order pair does not satisfy the inequalities then it comes in unshaded area. (for example (0,7) is the point outside the shaded area because 7<7 is false)

While, if a order pair satisfies the inequalities then it comes in shaded area. (for example (0,0) comes in the shaded area of the above inequality because 0<7 is true)