Question

A young woman wants to make at least $200 a week and can't work no more than 30 hours a week. she works at the library for $8 an hour and babysits for $6 an hour.

a. What system of inequalities shows the possible combination of hours and jobs she can work?
b. Why did you exclude points to the left of the y-axis and below the x-axis

Answer 1

Let, Number of Hours in Library = x
Number of Hours in babysitting = y

Inequality would be: x + y = 30 ;
& 8x + 6y ≥ 200

b) Solving: Multiply first equation by 6,
6x + 6y ≥ 180
Subtract it from 2nd equation,
2x ≥ 20
x ≥ 10

Now, substitute it in 1st equation,
10 + y = 30
y = 20

Your Answer would be (10, 20)
x - value is lesser or equal to 10, so it would move to left (decreasing direction)!

Hope this helps!